Unit 5: Rotation

The moment of inertia of a solid disk of mass M and radius R about its center is:

A solid sphere (I = ⅖MR²) of mass 2 kg and radius 0.1 m rolls without slipping. If its center moves at 3 m/s, what is the total kinetic energy in J?

The moment of inertia of a uniform thin rod of mass M and length L about an axis through one end is found by integration. The result is

A disk of mass M and radius R rolls without slipping down an incline of angle θ. The acceleration of the center of mass is

A torque [math] N·m is applied to a wheel with moment of inertia [math] kg·m². Starting from rest, the angular velocity at t = 4 s is

A uniform disk of mass M and radius R has moment of inertia [math] about its center. Using the parallel axis theorem, the moment of inertia about an axis at the rim is

The angular momentum of a particle of mass m moving in a circle of radius r with speed v is

The total kinetic energy of a solid sphere ([math]) of mass 2 kg rolling without slipping at 5 m/s is

The rotational analog of Newton's second law, [math], is

The moment of inertia of a uniform solid disk of mass M and radius R about its center is derived by integration as

A wheel starts from rest and undergoes angular acceleration [math] rad/s². The angular velocity at t = 4 s is

A uniform thin hoop of mass M and radius R has moment of inertia [math]. If it rolls without slipping down an incline, its acceleration is

A flywheel (moment of inertia 4 kg·m²) receives a torque that varies as [math] N·m. Starting from rest, the angular velocity when the torque reaches zero is

An ice skater spins with angular velocity ω and arms extended (I₁). Pulling arms in reduces moment of inertia to I₁/3. The new angular velocity is

A force of 20 N is applied perpendicular to a wrench 0.3 m from the bolt. What is the torque?

Which has the greater moment of inertia about its center: a solid disk or a thin ring of the same mass and radius?

An ice skater spinning with arms extended pulls her arms in. What happens to her angular velocity and angular momentum?

A wheel starts from rest and accelerates uniformly at 4 rad/s² for 3 seconds. What is its angular velocity?

For an object rolling without slipping, the relationship between linear velocity v and angular velocity ω is:

The rotational kinetic energy of a spinning object is: