RepetoWith Cartesian axes in an inertial frame, what scalar equation gives a constant-mass particle's x acceleration?
ΣFₓ = maₓ, using signed x components of all forces on the particle.
Classical mechanics: formulas and concepts
176 questions in English on Newtonian motion, forces, energy, momentum, rotation, orbits and oscillations, with stated assumptions.
- 176 cards
- By Repeto
- Free
What the cards look like
For fixed launch speed, equal launch and landing heights, level ground, constant g and no drag, which launch angle maximizes horizontal range?
45° above horizontal. Changing those assumptions can change the optimum.
What belongs on the free-body diagram of one selected object?
Every external force acting on it, with direction; omit forces it exerts on other objects and do not add acceleration as a force.
What does the signed area under a one-dimensional acceleration–time graph give?
The change in velocity over the interval.
How is one-dimensional instantaneous acceleration obtained from velocity v(t)?
a(t) = dv/dt = d²x/dt².
In Newtonian gravity, what is the direction of the force between two positive point masses?
Along the line joining them, attracting each mass toward the other.
All 176 cards
Every card in the deck, in study order.
Question Answer
With Cartesian axes in an inertial frame, what scalar equation gives a constant-mass particle's x acceleration? ΣFₓ = maₓ, using signed x components of all forces on the particle.
For fixed launch speed, equal launch and landing heights, level ground, constant g and no drag, which launch angle maximizes horizontal range? 45° above horizontal. Changing those assumptions can change the optimum.
What belongs on the free-body diagram of one selected object? Every external force acting on it, with direction; omit forces it exerts on other objects and do not add acceleration as a force.
What does the signed area under a one-dimensional acceleration–time graph give? The change in velocity over the interval.
How is one-dimensional instantaneous acceleration obtained from velocity v(t)? a(t) = dv/dt = d²x/dt².
In Newtonian gravity, what is the direction of the force between two positive point masses? Along the line joining them, attracting each mass toward the other.
At radius r outside a fixed spherically symmetric body of mass M, what minimum launch speed permits escape to infinity with zero final speed, ignoring drag and other bodies? v_escape = √(2GM/r).
Why may momentum conservation be a useful approximation during a brief collision even when external forces act? The external impulse during the short collision can be negligible compared with the collisional impulses.
A point on a rigid body rotates about a fixed axis at nonnegative angular speed ω and perpendicular distance r. What is its speed? v = rω.
For a particle moving under time-independent conservative forces only, what happens to E = K + U? E remains constant; kinetic and potential energy can change individually.
About a fixed origin in an inertial frame, what is the change in a system's angular momentum over an interval? ΔL = ∫τ_external dt, the net angular impulse about that origin.
For point masses m_i at perpendicular distances r_i from a chosen axis, what is their moment of inertia about that axis? I = Σm_i r_i², with SI units kg·m².
For a rigid body rotating about a fixed axis in an inertial frame with constant moment of inertia I, what relates net external torque along that axis to α? Στ_axis = Iα, with a consistent signed axis convention.
For an unforced oscillator subject to resistive damping, what happens to its mechanical energy over time? It decreases as damping transfers mechanical energy to other forms; oscillations, if present, decay.
For point masses M and m separated by r, choosing gravitational potential energy zero at infinite separation, what is U(r)? U = −GMm/r.
In a uniform downward gravitational field with magnitude g and upward coordinate y, how does gravitational potential energy change? ΔU = mg(y_f − y_i).
In a one-dimensional elastic collision of two equal masses with negligible external impulse, how do their final velocities relate to their initial velocities? They exchange velocities.
Does zero instantaneous velocity imply zero instantaneous acceleration? No. At the top of a vertical throw without drag, velocity is momentarily zero while acceleration is downward.
A block slides on a surface with normal force 80 N and μₖ = 0.25. In the dry-friction model, what is friction's magnitude? 20 N, from 0.25 × 80.
A vehicle follows a horizontal circle of radius r on a frictionless banked road at angle θ to horizontal. With gravity g, what speed requires no friction? v = √(rg tan θ), assuming sustained contact and no vertical acceleration.
For fixed-axis rotation with constant signed α and angular velocity ω₀ at t = 0, what is ω(t)? ω = ω₀ + αt.
A person of mass m stands on a horizontal elevator floor accelerating upward at a. With gravity magnitude g and no other vertical forces, what is N? N = m(g + a), from N − mg = ma.
For a closed system of constant total mass M in an inertial frame, what determines center-of-mass acceleration? ΣF_external = M a_CM; internal force pairs cancel in the total-force balance.
What distinguishes an elastic collision when external impulse is negligible? Total momentum and total kinetic energy are both unchanged across the collision.
A block stays in contact with a straight incline angled θ above horizontal. If only gravity and contact forces act and perpendicular acceleration is zero, what is N? N = mg cos θ.
Outside a spherically symmetric mass distribution of total mass M, what point-mass model reproduces its gravitational field? A point mass M at its center; r is distance from that center, not height above the surface.
Point masses 1 kg at x = 0 m and 3 kg at x = 8 m form a system. Where is its center of mass? x_CM = 6 m, from (1 × 0 + 3 × 8)/(1 + 3).
When net force on a rigid body is zero, how does the net torque depend on the choice of origin? It is the same about every origin, so a convenient pivot can simplify an equilibrium calculation.
If x(t) = A cos(ωt + φ) for an ideal oscillator, what is its signed velocity? v(t) = −Aω sin(ωt + φ).
How is a force's torque magnitude about an origin related to its perpendicular lever arm d? The magnitude is Fd; d is the perpendicular distance from the origin to the force's line of action.
For a particle with conservative forces represented by time-independent U, how does work by the remaining forces affect K + U? W_nonconservative = Δ(K + U).
Outside a spherically symmetric body of mass M, what is gravitational acceleration magnitude at center-to-point distance r? g(r) = GM/r², directed toward the center.
Can an isolated system initially at rest gain total kinetic energy when it breaks apart? Yes. Stored internal energy can become kinetic energy while the vector sum of momenta remains zero.
For a projectile in uniform vertical gravity with no drag, how do horizontal and vertical motions couple? They share the same elapsed time, but their component equations can be solved independently.
A motor does 900 J of mechanical work in 6 s. What is its average mechanical power? 150 W, from 900/6.
In Newtonian mechanics, how is the velocity of A relative to B found from velocities measured in the same inertial frame? v_A/B = v_A − v_B, using vector subtraction.
For a rigid body rotating about a fixed axis with moment of inertia I and angular speed magnitude ω, what is its kinetic energy? K_rot = ½Iω².
For one-dimensional motion under a potential U(x) that is constant throughout a neighborhood, what kind of equilibrium occurs there? Neutral equilibrium: a displacement within that region creates no restoring or destabilizing force.
For a rigid body of mass M, how does moment of inertia about an axis compare with a parallel axis through its center of mass, distance d away? I = I_CM + Md².
For fixed-axis rotation with constant signed α, initial angle θ₀ and angular velocity ω₀, what is θ(t)? θ = θ₀ + ω₀t + ½αt².
For a force F applied at position vector r from a chosen origin, what is its torque about that origin? τ = r × F, with direction given by the right-hand rule.
Outside a spherically symmetric body, gravitational acceleration is g₀ at radius r₀ from its center. What is it at radius 3r₀? g₀/9, because acceleration scales as 1/r².
For an ideal Hookean spring with constant k and extension x from its natural length, choosing U = 0 at x = 0, what is U? U = ½kx², for either stretch or compression within the Hookean range.
In an inertial-frame free-body diagram for circular motion, is centripetal force an additional interaction? No. It names the inward net force component, supplied by actual interactions such as tension, friction or gravity.
A cart initially moves at +12 m/s with constant acceleration −3 m/s² until rest. What is its displacement? +24 m, from (0² − 12²)/(2 × −3).
About a fixed origin in an inertial frame, what condition guarantees constant total angular momentum throughout an interval? Zero net external torque about that origin throughout the interval.
In a quadratic-drag model, how is drag magnitude related to fluid-relative speed v? F_D = ½ρC_DAv², where ρ is fluid density, A reference area and C_D the corresponding dimensionless coefficient.
For motion along one axis with constant acceleration a, what equation links velocities and displacement without time? v² = v₀² + 2a(x − x₀). Squaring loses the velocity sign.
What is the general displacement of an ideal one-dimensional simple harmonic oscillator with amplitude A and angular frequency ω? x(t) = A cos(ωt + φ), where φ sets the phase from initial conditions.
For an undamped horizontal Hookean mass–spring oscillator of stiffness k and amplitude A, with potential zero at equilibrium, what is total mechanical energy? E = ½kA²; it alternates between kinetic and spring potential energy.
For a bound test mass orbiting a fixed point mass under Newtonian gravity, what is the orbital shape when angular momentum is nonzero? An ellipse, with the attracting mass at one focus; a circle is the equal-axis special case.
For uniform circular motion of radius r and period T, how is speed related to T? v = 2πr/T.
A test mass follows a circular orbit of radius r outside a fixed spherically symmetric body of mass M. Under Newtonian gravity alone, what is its speed? v = √(GM/r), with r measured from the source's center.
For a vector with perpendicular Cartesian components Aₓ and Aᵧ, what is its magnitude? A = √(Aₓ² + Aᵧ²), a nonnegative scalar.
Why do the two forces in a Newton third-law pair not cancel on a single body's free-body diagram? They act on different bodies; a free-body diagram includes only forces acting on the chosen body.
For a circular arc of length s and radius r, how is the subtended angle θ expressed in radians? θ = s/r; radians are dimensionless, although rad is retained to identify angular quantities.
For a projectile under constant downward gravity without drag, what is vᵧ(t) if +y is upward? vᵧ = v₀ᵧ − gt.
For a body moving through a fluid, which velocity determines the opposing direction of drag? The body's velocity relative to the surrounding fluid, not necessarily its velocity relative to the ground.
A 3 kg particle moves at 4 m/s in a specified inertial frame. What is its kinetic energy? 24 J, from ½ × 3 × 4².
What characterizes an inertial reference frame in Newtonian mechanics? A free particle has constant velocity in that frame; no fictitious force is needed to apply Newton's laws.
Show the other 116 cards
For rotation about a symmetry axis with fixed nonzero angular momentum L, how does kinetic energy depend on moment of inertia I? K_rot = L²/(2I); reducing I increases rotational kinetic energy. The increase is supplied by work, which need not be internal even when external torque is zero.
A projectile launches horizontally from 45 m above level ground. With no drag and g = 10 m/s², how long until impact? 3 s, from t = √(2 × 45/10).
For periodic motion with period T and angular frequency ω, what is ordinary frequency f? f = 1/T = ω/(2π), measured in hertz.
When is tension uniform along an ideal rope passing over an ideal pulley? For a massless taut rope and a frictionless pulley with negligible rotational inertia.
What force condition gives zero center-of-mass acceleration for a rigid body in an inertial frame? ΣF_external = 0; translational equilibrium can include constant nonzero center-of-mass velocity.
Why is the normal force on an object not always equal to mg? It follows from the perpendicular force balance; slopes, other forces or perpendicular acceleration can change it.
For a test mass in a circular Newtonian orbit of radius r around a fixed point mass M, what is the period? T = 2π√(r³/(GM)).
For particles with masses m_i at position vectors r_i and total mass M, what is their center-of-mass position? R_CM = Σ(m_i r_i)/M.
A uniform horizontal beam of weight 100 N rests on supports at its two ends, with no other load. What is the upward force at each support in static equilibrium? 50 N at each end, from symmetry and vertical force balance.
For a rigid body rotating about a fixed axis with moment of inertia I, what is its angular-momentum component along that axis? L_axis = Iω. The full vector L need not be parallel to ω for an arbitrary axis.
For a particle with momentum p at position r relative to a chosen origin, what is its angular momentum about that origin? L = r × p, with SI units kg·m²/s.
A rotor spinning about a fixed symmetry axis has I = 3 kg·m² and ω = +4 rad/s. What is its axial angular momentum? +12 kg·m²/s, from Iω.
For a circular wheel whose center of mass lies on its geometric axis, rolling without slipping along a stationary straight surface, what relates center-of-mass speed v_CM and angular speed ω? v_CM = Rω, where R is the wheel radius.
A 0.20 kg ball changes x velocity from +15 m/s to −10 m/s. What is its net x impulse? −5 N·s, from 0.20(−10 − 15).
A particle moves at 6 m/s around a circle of radius 3 m. What is the radial acceleration magnitude? 12 m/s² inward, from 6²/3.
In the simple dry-friction model, what inequality constrains static-friction magnitude fₛ for normal force N? 0 ≤ fₛ ≤ μₛN; it takes the value needed to prevent slipping, up to that limit.
For a force F acting on a particle moving with velocity v, what is its instantaneous power? P = F·v; the sign indicates energy transfer into or out of the particle's kinetic energy by that force.
A boat moves north at 4 m/s relative to water flowing east at 3 m/s. What is its speed relative to shore? 5 m/s, from √(4² + 3²); its shore velocity points northeast.
A 4 kg cart experiences +18 N and −6 N along a horizontal axis in an inertial frame, with no other horizontal force. What is aₓ? +3 m/s², from (18 − 6)/4.
For a constant-mass particle in an inertial frame, how does net work relate to kinetic energy? W_net = K_f − K_i; include work by every force acting on the particle.
A stationary block is pushed right with 7 N on a horizontal surface. Static friction can reach 12 N and no other horizontal forces act. What is the friction force? 7 N left; the limiting 12 N is not reached.
For a test mass orbiting a fixed point mass under gravity alone, what does Kepler's second law say about the radius vector? It sweeps equal areas in equal times; orbital speed is greater closer to the source.
For rotation about a fixed axis with signed angular velocity ω(t), how is signed angular acceleration defined? α = dω/dt, conventionally in rad/s².
What is the net mechanical effect of two equal, opposite, parallel forces whose lines of action are separated by distance d? Zero net force and torque magnitude Fd; this pair is a force couple.
A rigid circular body whose center of mass lies on its geometric axis rolls without slipping down a fixed straight incline of angle θ under gravity and contact forces only. What is its center-of-mass acceleration downhill? a_CM = g sin θ/(1 + I_CM/(MR²)), assuming enough static friction and negligible rolling resistance.
For ideal simple harmonic motion of amplitude A and angular frequency ω, what is the maximum speed? v_max = Aω, reached at equilibrium.
For a nonrelativistic particle of mass m and velocity v in a specified frame, what is its momentum? p = mv, a vector with SI units kg·m/s.
How is work calculated when a force varies along a particle's path? W = ∫F·dr along the actual path.
A force of magnitude 12 N acts with perpendicular lever arm 0.25 m about an origin. What is the torque magnitude? 3 N·m, from 12 × 0.25.
Why should the small-angle pendulum period formula not be treated as amplitude-independent at large swings? The approximation sin θ ≈ θ fails; the period grows with amplitude for an ideal librating pendulum.
For a test mass m in a circular Newtonian orbit of radius r about a fixed point mass M, with U = 0 at infinity, what is total mechanical energy? E = −GMm/(2r).
A projectile launches upward at speed v₀ and angle θ and lands at its launch height. With constant g and no drag, what is its nonzero flight time? T = 2v₀ sin θ/g, for 0 < θ < 90°.
With constant signed acceleration a and initial velocity v₀ at t = 0, what is v(t)? v = v₀ + at.
For one-dimensional motion under a smooth time-independent potential U(x), what local potential shape gives unstable equilibrium? A local maximum: a small displacement lowers U and drives the particle farther away.
How is average speed calculated for a journey that may reverse direction? Total distance traveled divided by elapsed time; use distance, not the magnitude of net displacement.
A body falls vertically in still fluid with drag magnitude bv, constant g and negligible buoyancy. What terminal speed follows from this linear model? v_t = mg/b, where b > 0; at terminal speed drag balances weight.
For a particle following a circle of radius r with instantaneous speed v, what is the radial acceleration? Its magnitude is v²/r and its direction is toward the center.
For a point at perpendicular distance r from a fixed rotation axis, how is tangential acceleration related to signed angular acceleration α? a_t = rα, using the matching positive tangential direction.
What is the gravitational force magnitude between point masses M and m separated by distance r? F = GMm/r², where G is the universal gravitational constant.
At a dry contact, what determines the direction of static or kinetic friction? It opposes impending or actual relative sliding at the contact, which need not oppose the object's motion relative to the ground.
In a collision with negligible external impulse, what distinguishes an inelastic collision? Total momentum is conserved but total kinetic energy is not; energy is transferred to or from other forms.
For a rigid body at rest to remain in static equilibrium, what torque condition is required in addition to zero net force? Στ_external = 0 about any chosen fixed origin.
What does the signed area under a one-dimensional velocity–time graph give? Displacement over the interval; regions below zero contribute negatively.
What are the SI base units of one newton, using F = ma? 1 N = 1 kg·m/s².
For a test mass in a fixed Newtonian inverse-square gravitational field with U = 0 at infinity, what energy sign indicates a bound orbit? Negative total mechanical energy, E = K + U < 0.
For test masses in elliptical Newtonian orbits around the same fixed point mass M, how does period depend on semimajor axis a? T² = 4π²a³/(GM); thus T²/a³ is the same for those orbits.
Why does zero net force alone not ensure a rigid body remains at rest? A nonzero net torque can start its rotation even when its center of mass has zero acceleration.
A mass m hangs at rest from an ideal vertical spring of stiffness k in uniform gravity. What is its extension from natural length? x_eq = mg/k, within the Hookean range.
A projectile has positive initial upward velocity v₀ᵧ. With constant g and no drag, how far above its launch point does it rise? H = v₀ᵧ²/(2g).
A displacement has components +5 m east and +12 m north. What is its magnitude? 13 m, from √(5² + 12²).
Two masses m₁ and m₂ with initial velocities v₁ and v₂ stick together with negligible external impulse. What is their common final velocity? v_f = (m₁v₁ + m₂v₂)/(m₁ + m₂), using vectors or consistently signed one-dimensional velocities.
Frames S and S′ share an origin at t = 0, with S′ moving at constant +u along x. What is x′ in Newtonian mechanics? x′ = x − ut, with t′ = t.
Near Earth's surface with +y upward, constant gravitational magnitude g and negligible air resistance, what is vertical acceleration? aᵧ = −g during both ascent and descent.
For a conservative force in a simply connected region, what is the work around a closed path? Zero; its work between two points is independent of the path.
A rigid object rests on a horizontal support with gravity as its only applied load and no adhesion. What geometric condition is necessary to avoid gravitational tipping? The vertical projection of its center of mass must lie within the support area; its boundary is the tipping threshold.
With constant gravity and no drag, how do a projectile's speeds compare at two points at the same height? Their speed magnitudes are equal, although their velocity directions can differ.
For a vector of magnitude A at angle θ counterclockwise from +x in the xy plane, what are its components? Aₓ = A cos θ and Aᵧ = A sin θ.
For a constant force F acting through displacement Δr, what scalar gives its work? W = F·Δr = FΔr cos θ, where θ is the angle between force and displacement.
A 2 kg cart moving at +6 m/s sticks to a stationary 4 kg cart. With negligible external impulse, what is their common final velocity? +2 m/s, from (2 × 6 + 4 × 0)/(2 + 4).
For motion around a fixed circle with changing speed, what tangential acceleration accompanies the inward radial acceleration? With v denoting speed, a_t = dv/dt when the positive tangent follows the instantaneous direction of motion. A negative value means acceleration opposite the motion.
In the simple dry-friction model, what is the magnitude of sliding friction for normal force N? fₖ = μₖN, using the kinetic-friction coefficient for the contacting surfaces.
In straight vertical descent at constant terminal velocity through still fluid, what is the net force? Zero; acceleration is zero even though the body is moving.
For an ideal rigid wheel rolling without slipping on a stationary rigid surface, what work does static friction do at the instantaneous contact point? Zero, because that contact point has zero velocity; rolling resistance and deformation are excluded.
A cart has v₀ = +7 m/s and constant a = −2 m/s² for 3 s. What is its final velocity? +1 m/s, from 7 − 2(3).
A block slides distance s on a fixed straight surface with constant kinetic-friction magnitude fₖ opposing motion. What work does friction do on the block? W_f = −fₖs; the negative sign reflects energy removed from the block's mechanical motion.
For a point bob on a massless inextensible string of length ℓ, with small angular swings, uniform g and negligible drag, what is its period? T ≈ 2π√(ℓ/g). The small-angle approximation requires angular amplitude much less than 1 radian.
Why do internal interaction forces not change a system's total linear momentum in Newtonian mechanics? Their equal-and-opposite third-law pairs cancel when forces on all system members are summed.
What impulse does a constant force F deliver over time interval Δt? J = FΔt, with the same direction as the force and SI units N·s.
How does work W_c by a conservative force relate to the change in its associated potential energy? W_c = −ΔU.
A body falls vertically in still fluid with constant ρ, C_D, A and g, negligible buoyancy and drag ½ρC_DAv². What is terminal speed? v_t = √(2mg/(ρC_DA)).
For ideal simple harmonic motion of angular frequency ω, how is acceleration related to displacement x from equilibrium? a = −ω²x.
On a flat road, static friction alone supplies a vehicle's radial force. With coefficient μₛ, radius r and no other vertical force besides weight and normal force, what is the maximum no-slip speed? v_max = √(μₛgr), in the simple friction model.
For one-dimensional motion under a smooth time-independent potential U(x), what local potential shape gives stable equilibrium? A local minimum: a small displacement raises U and produces a restoring tendency.
For one-dimensional motion with nonzero velocity and acceleration, how do the signs of v and a determine whether speed increases? Equal signs mean increasing speed; opposite signs mean decreasing speed.
A block slides on a fixed frictionless incline at angle θ above horizontal. With downhill positive and no other forces, what is its acceleration? a = g sin θ downhill.
How does a particle's acceleration compare in two nonrotating inertial frames moving at constant velocity relative to each other? The acceleration vector is the same in both frames.
For a constant-mass particle with displacement x from stable equilibrium, what net-force law produces ideal simple harmonic motion? F_net = −kx with constant k > 0; force is proportional to displacement and points toward equilibrium.
A projectile launches at speed v₀ and angle θ above horizontal. With no drag and constant vertical gravity, what is vₓ(t)? vₓ = v₀ cos θ, constant throughout the flight.
For a nonrelativistic particle of constant mass m and speed v in a specified inertial frame, what is kinetic energy? K = ½mv², a nonnegative scalar measured in joules.
For a system measured about a fixed origin in an inertial frame, how does net external torque relate to total angular momentum? Στ_external = dL/dt, about that same origin.
In uniform vertical gravity without drag, what shape is a projectile's trajectory when its horizontal velocity is nonzero? A parabola in the vertical plane containing the motion.
A projectile launches at 20 m/s and 30° above horizontal, returning to its launch height. With no drag and g = 10 m/s², what is its range? 20√3 m ≈ 34.6 m, from 20² sin 60°/10.
What is the moment of inertia of a uniform solid disk of mass M and radius R about its central symmetry axis? I = ½MR².
A projectile starts at y₀ with upward velocity component v₀ᵧ. With +y upward, constant g and no drag, what is y(t)? y = y₀ + v₀ᵧt − ½gt².
How is the dot product of vectors A and B related to their magnitudes and included angle θ? A·B = AB cos θ; the result is a scalar.
A projectile launches at speed v₀ at angle θ above horizontal and lands at the same height. With constant g and no drag, what is its horizontal range? R = v₀² sin(2θ)/g, for 0 < θ < 90°.
What distinguishes a vector quantity from a scalar quantity in mechanics? A vector has magnitude and direction and obeys vector addition; a scalar has magnitude without a spatial direction.
A rotating system has negligible external torque about its fixed rotation axis. If its moment of inertia decreases, how does angular speed change? Angular speed increases so that Iω remains constant.
An ideal undamped oscillator has mass 2 kg and spring stiffness 50 N/m. What is its period? T = 2π√(2/50) = 0.4π s ≈ 1.26 s.
How are the magnitude and direction of A × B determined for nonzero, nonparallel vectors with included angle 0 < θ < π? Its magnitude is AB sin θ; its perpendicular direction follows the right-hand rule from A toward B.
An ideal spring has k = 200 N/m and is stretched 0.10 m from its natural length. With zero potential energy at natural length, what energy is stored? 1 J, from ½ × 200 × 0.10².
In a uniform gravitational field, where does a rigid body's center of gravity lie relative to its center of mass? They coincide; the total gravitational torque can be represented by its weight acting there.
For one-dimensional motion over a nonzero interval Δt, how is average velocity defined? v_avg = (x_f − x_i)/Δt; its sign follows the chosen x axis.
What SI base units describe mass, length and time in Newtonian mechanics? Kilogram (kg), metre (m) and second (s), respectively.
In a local gravitational field g, what vector expression gives the weight of mass m? W = mg, directed with the gravitational field; weight is a force measured in newtons.
A constant 10 N force acts at 60° to a straight 3 m displacement. What work does this force do? 15 J, from 10 × 3 × cos 60°.
How is average power supplied by a force over a time interval Δt defined? P_avg = W/Δt, measured in watts (joules per second).
When acceleration is constant over an interval, what is the average velocity in terms of endpoint velocities? v_avg = (v_i + v_f)/2.
A rigid rotor has I = 2 kg·m² about its fixed rotation axis and angular speed 3 rad/s. What is its rotational kinetic energy? 9 J, from ½ × 2 × 3².
For rotation about a fixed axis with signed angle θ(t), how is signed angular velocity defined? ω = dθ/dt, conventionally in rad/s.
With constant signed acceleration a and initial position x₀ and velocity v₀ at t = 0, what is x(t)? x = x₀ + v₀t + ½at².
What work does a force do when it remains perpendicular to a particle's instantaneous displacement throughout the motion? Zero work, because F·dr = 0 along the path.
For a constant-mass particle in an inertial frame, what vector equation connects net force and acceleration? ΣF = ma, where ΣF is the vector sum of forces acting on that particle.
In an inertial frame, what does zero net force imply for a constant-mass particle's velocity? Its velocity remains constant; it need not be at rest.
If both sides of a proposed mechanics equation have the same dimensions, what has been established? Dimensional consistency only; the equation can still have a wrong sign, numerical factor or physical assumption.
Under the same uniform gravity with no air resistance, do two released objects of different masses have different accelerations? No. Both have the same gravitational acceleration, independent of their masses.
How does net impulse on a constant-mass particle relate to its momentum change in an inertial frame? J_net = ∫F_net dt = Δp, a vector equality.
For a rigid wheel translating at speed v_CM and rotating about its center with angular speed ω, what is its total kinetic energy? K = ½Mv_CM² + ½I_CMω², using the central rotation axis.
What is the moment of inertia of a uniform thin rod of mass M and length L about an axis through its center perpendicular to the rod? I = ML²/12.
Why must an axis be specified when quoting a body's moment of inertia? Moment of inertia depends on how its mass is distributed by perpendicular distance from that axis.
For mass m attached to an ideal massless spring of stiffness k, with no damping and motion about equilibrium, what is angular frequency? ω = √(k/m).
How is one-dimensional instantaneous velocity obtained from position x(t)? v(t) = dx/dt, the slope of the position–time graph.
For a closed system in an inertial frame, what condition keeps total linear momentum constant throughout an interval? Zero net external force throughout the interval; internal forces exchange momentum within the system.
A massless horizontal lever pivots at its center. A 30 N downward force acts 0.40 m left of the pivot. What downward force 0.60 m right balances its torque? 20 N, from 30 × 0.40 = F × 0.60.
For a weakly damped linear oscillator driven by a sinusoidal force of fixed amplitude, when is its steady-state displacement amplitude largest? Near its natural frequency; finite damping limits the amplitude and shifts the exact peak.
A block rests on a fixed incline under gravity and contact forces only. In the dry-friction model, what angle marks impending downward slip? tan θ = μₛ at the threshold, for 0 ≤ θ < 90°.
How you study it in Repeto
- Install the deck free. It lands in your library on the web, iPhone, iPad and Mac.
- Answer from memory. See the front, recall the answer, then flip and rate how it went.
- Review at the right time. FSRS spaced repetition brings each card back just before you would forget it, so a few minutes a day is enough.
Sources and license
Original Repeto study-card text. Educational diagrams and museum images retain the source, creator and license attribution recorded on each card and in the documented source manifest.