AP Physics C: Mechanics Easy practice

A mass–spring system has spring constant $k=400$ N/m and mass $m=1$ kg. What is the angular frequency of oscillation?

A ball is launched horizontally from a cliff 80 m high with speed $20$ m/s. Using $g=10$ m/s², how far from the base of the cliff does it land?

A uniform solid disk of mass $M$ and radius $R$ has moment of inertia about its central axis $I=\frac{1}{2}M{R}^2$. A net torque $\tau =4$ N·m is applied to a disk with $M=2$ kg and $R=1$ m. What is the angular acceleration?

A solid cylinder ($I=\frac{1}{2}M{R}^2$) rolls without slipping down a frictionless incline of height $h$. Using energy conservation, find the speed at the bottom.

Using Kepler's third law $T^2\propto r^3$, if Earth's orbital radius is $1$ AU and period is $1$ yr, what is the orbital period of a planet at $4$ AU?

A simple pendulum of length $L=1$ m oscillates with small amplitude. What is its period? ($g=10$ m/s²)

A wheel starts from rest and reaches an angular velocity of $10$ rad/s in $5$ s under constant angular acceleration. What is the angular acceleration?

A spring with constant $k=200$ N/m is compressed 0.1 m from its natural length. How much elastic potential energy is stored?

A particle of mass $m=0.5$ kg moves in a circle of radius $r=2$ m at speed $v=4$ m/s. What is its angular momentum about the center?

A 1 kg ball moving at $6$ m/s to the right undergoes a perfectly inelastic collision with a stationary 2 kg ball. What is their combined velocity after the collision?

A 2 kg block hangs from a rope attached to the ceiling. What is the tension in the rope? ($g=10$ m/s²)

A satellite of mass $m$ orbits Earth (mass $M_E$, radius $R_E$) at altitude $h$ above the surface in a circular orbit. What is the orbital speed?

A constant force $F=8$ N acts on a 2 kg object for 3 s. What is the change in velocity?

A 3 kg object moves from rest and reaches a speed of $4$ m/s. What is the net work done on it?

Two blocks, $m_1=3$ kg and $m_2=5$ kg, are connected by a massless rope and pulled across a frictionless surface by a force $F=16$ N applied to $m_2$. What is the tension in the rope between them?