Torque and Rotational Motion

6 radians

40 radians

20 radians

14 radians

Final rotational speed will be two times larger than originally observed.

Final rotational speed will remain unchanged from original observations.

Final rotational speed will be eight times larger than originally observed.

Final rotational speed will be four times larger than originally observed.

The disk arrives first, showing it has a smaller moment of inertia than the hoop for rolling motion.

They arrive at the same time, indicating that mass distribution does not affect rolling motion.

The disk arrives first, demonstrating that its center of mass falls faster due to its shape.

The hoop arrives first, showing it has a larger moment of inertia than the disk for rolling motion.

It will come to a stop immediately.

It will increase its angular velocity.

It will rotate with increasing angular acceleration.

It will continue rotating at constant angular velocity.

Only thermal energy

Only gravitational potential energy

Only kinetic energy

Both linear and angular momenta

$\omega_f \equiv \omega_i + \alpha t$

$x_f = x_i + v_i t + \frac{1}{2} \alpha t^2$

$s = r \theta$

$a_c = r \alpha t^2$

2 rad/s

8 rad/s

4 rad/s

3 rad/s

Moment of inertia

Angular momentum

Tangential speed

Centripetal acceleration

Kilograms times meters squared (kg·m^2)

Meters per second squared (m/s^2)

Newton-meter (N·m)

Radians per second (rad/s)

The total angular momentum of the system decreases over time.

The total angular momentum of the system remains constant.

The total angular momentum of the system increases over time.

The total linear momentum of the system remains constant.