Torque and Rotational Motion

Only thermal energy

Only gravitational potential energy

Only kinetic energy

Both linear and angular momenta

It decreases.

It reverses direction.

It increases.

It stays the same.

Angular velocity increases as internal friction provides additional torque converting potential energy into rotational kinetic energy.

Rotational kinetic energy maintains constant while potential energy oscillates between maximums and minimums because there's no net force.

The total kinetic energy increases since conversion from static friction back to kinetic friction adds energy into the rotational system.

Total kinetic energy decreases since friction converts some rotational kinetic energy into thermal energy over time.

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

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

$s = r \theta$

$a_c = r \alpha t^2$

Total linear momentum

Total mechanical energy

Kinetic energy of both objects

Velocity of the putty ball

There isn't enough information to determine what happens to the rotational speed.

The rotational speed increases.

The rotational speed decreases.

The rotational speed remains unchanged.

2 rad/s

8 rad/s

4 rad/s

3 rad/s

The particle with less charge moves faster since it has a lower mass/charge ratio and experiences less resistance

The particle with greater charge has a higher angular velocity because it experiences greater force

They are the same because charge has no effect on angular velocity once particles are released

The twice-charged particle will stop first due to greater interaction with field lines leading to slower angular velocity after release

Moment of inertia

Angular momentum

Tangential speed

Centripetal acceleration

Weight cannot be determined without knowing specific altitudes involved and Earth’s radius precisely as well as local variations in Earth’s density and shape such as mountains or valleys could affect measurements too much for a simple inverse-square law approximation.

The object at twice this altitude experiences less weight due to weaker gravity.

Both objects experience equal weights since their masses are equal.

The object at sea level experiences less weight because it is closer to Earth's center.