A 0.2 kg particle moves in a conservative force field where the potential energy function is $$U(x) = 3x^2 - 2x^3$$ (in joules, with $$x$$ in meters). If the particle has a total mechanical energy of 5 J, at what value of $$x$$ does it have maximum kinetic energy?

A 2.0 kg object moving at 5.0 m/s collides with a wall and rebounds with a speed of 3.0 m/s in the opposite direction. If the collision lasts for 0.02 seconds, what is the magnitude of the average force exerted on the object during the collision?

In the context of SHM, what does the angular frequency `ω` determine?

A 2.0 kg object is in free fall. What is its apparent weight during the fall?

What is the rotational inertia of a point mass `m` at distance `r` from the axis?

A 0.5 kg ball is thrown horizontally with velocity 8.0 m/s. It strikes a vertical wall and rebounds with velocity 6.0 m/s in the opposite direction. If the collision lasts 0.02 seconds, what is the average force exerted on the ball during the collision?

What is the formula for average acceleration?

A uniform disk of radius R and mass M is placed on a rough horizontal surface. A horizontal force F is applied at height h above the center of the disk. For what value of h will the disk roll without slipping?

A uniform disk of mass M and radius R has initial angular velocity ω₀. It is placed on a horizontal surface where friction gradually brings it to rest. If the coefficient of kinetic friction is μ, what is the total work done by friction?

A mass-spring system has a period of 0.4 s. If the spring constant is quadrupled and the mass is doubled, what will be the new period of the system?

A 0.5 kg ball is thrown horizontally at 15 m/s. Air resistance exerts a constant force of 2.0 N opposite to the motion for 1.5 s before the ball hits a wall. What is the magnitude of momentum transferred from the ball to the environment during this time?

A 1500 kg car traveling at 20 m/s crashes into a wall and comes to a stop in 0.1 seconds. During the collision, the crumple zone of the car compresses by 0.8 meters. What is the average force exerted on the car during this collision?

When is the acceleration of a simple harmonic oscillator zero?

A wheel rotating counterclockwise at 10 rad/s experiences an angular acceleration of 2 rad/s² in the clockwise direction. How long will it take for the wheel to come to a momentary stop?

A particle of mass m moves in a medium with a velocity‑dependent resistive force Fr⃗ = −kv⃗. If the particle has initial velocity v₀ and no other forces act on it, what fraction of its initial kinetic energy remains after it moves for a time equal to m/k?

A satellite orbits Earth in a circular path. A problem asks for the net force on the satellite without specifying a reference frame. Which of the following is the correct approach?

A solid sphere of radius R rolls without slipping down an inclined plane. At an instant when its center of mass has linear acceleration acm, what is the angular acceleration of the sphere?