Physics C: Mech math practice

Every skill in this set

Kinematics: final velocityKinematics

v = v₀ + at

Pick the equation that leaves out the quantity you neither have nor want. This one omits displacement, so it is the right choice whenever distance is not mentioned.

Kinematics: displacementKinematics

Δx = v₀t + ½at²

The ½at² term is where sign errors hide. If acceleration opposes the initial velocity, the object can end up behind where it started even while moving forward at first.

Newton's second lawForce & Translational Dynamics

ΣF = ma

The F in this equation is the NET force. Adding one force and dividing by mass gives the wrong answer whenever more than one force acts, which is nearly always.

Impulse and momentum changeLinear Momentum

J = FΔt = Δp = mΔv

Impulse is the bridge between force and velocity change. Airbag and follow-through questions are all the same: extend Δt to reduce F for a fixed Δp.

Work-energy theoremEnergy

W_net = ΔKE = ½mv² − ½mv₀²

Kinetic energy goes with the square of speed, so doubling speed quadruples the energy — and quadruples the stopping distance for a given braking force.

Centripetal accelerationCircular Motion & Gravitation

a_c = v² / r · F_c = mv² / r

Centripetal force is not a new force — it is whatever real force points at the center. Naming that force (tension, friction, gravity, normal) is usually where the marks are.

Projectile: time of flightKinematics

horizontal and vertical motion are independent

The horizontal velocity never affects the fall time. A ball fired horizontally and one dropped from the same height land together, and this calculation is why.

Torque and rotational equilibriumTorque & Rotational Dynamics

τ = rF sin θ

Only the component of force perpendicular to the lever arm produces torque. A force pointing along the arm produces none at all, whatever its magnitude.

Simple harmonic motion: periodOscillations

T = 2π√(m/k) · T = 2π√(L/g)

The period of a mass on a spring does not depend on amplitude, and the period of a pendulum does not depend on mass. Both are standard multiple-choice traps.

Conservation of angular momentumEnergy and Momentum of Rotating Systems

I₁ω₁ = I₂ω₂

Angular momentum is conserved when the net external torque is zero — not when the net force is zero. Reduce the rotational inertia and the angular speed must rise to compensate, which is the whole content of the spinning-skater problem.

Rolling descent: speed at the bottomEnergy and Momentum of Rotating Systems

mgh = ½(1 + c)mv² → v = √(2gh / (1 + c))

A rolling object splits its energy between translation and rotation, so it arrives slower than a sliding block. Mass and radius cancel completely — only the drop height and the shape coefficient c matter.

Buoyancy: floating fraction and apparent weightFluids

F_b = ρ_fluid V g · V_sub/V_total = ρ_object/ρ_fluid

The submerged fraction of a floating object is nothing but the ratio of the two densities — size, shape and mass all cancel. Apparent weight is then a one-line force balance.

Continuity and Bernoulli in a pipeFluids

A₁v₁ = A₂v₂ · P + ½ρv² + ρgh = constant

Continuity comes first: it converts the two unknown speeds into one. Note that area goes as the square of the radius, so halving the radius quadruples the speed rather than doubling it.

Common questions