Exploring Rotational Kinetic Energy

What is the formula for the rotational kinetic energy of a rigid body rotating about a fixed axis?

Which of the following quantities is directly proportional to the torque applied to a rotating object?

• Angular velocity

• Angular acceleration

• Rotational kinetic energy

• Moment of inertia

• It remains the same

• It doubles

• It quadruples

• It halves

If a disk and a ring have the same mass and radius, which one has a greater moment of inertia?

• The disk

• The ring

• They have the same moment of inertia

• It depends on the axis of rotation

A solid sphere and a hollow sphere have the same mass and radius. Which one will have a higher rotational kinetic energy if both are rotating with the same angular velocity?

• The solid sphere

• The hollow sphere

• They will have the same rotational kinetic energy

• It depends on the distribution of mass

What is the relationship between torque and angular momentum for a rotating object?

• Torque is the rate of change of angular momentum

• Torque is the product of angular momentum and time

• Torque is the sum of angular momentum and force

• Torque is the difference between angular momentum and force

Which of the following applications involves the use of rotational kinetic energy?

• A car accelerating in a straight line

• A spinning top

• A pendulum swinging

• A block sliding down an incline

If the moment of inertia of a rotating object is increased while keeping the angular velocity constant, what happens to the rotational kinetic energy?

• It increases

• It decreases

• It remains the same

• It becomes zero

Which of the following is an example of torque in everyday life?

• Pushing a door open

• Lifting a box straight up

• Sliding a book across a table

• Dropping a ball