Angular Momentum

1) An object with more _______________________ will be more difficult to spin, but once it gets spinning it will be harder to stop.

2) A(n) _______________________ is needed to change an object’s rotation.

3) Moving an object’s mass farther from its rotational axis increases its _______________________ .

4) Imagine you were to look down upon a spinning child’s toy, and it is rotating counter-clockwise. What is the direction of its angular velocity? If the toy were slowing in its rotation, what direction is its angular acceleration?

5) If a ball spins 3.0 times in 1.2 seconds, what is its angular speed? Give your answer in both rotations/second and radians/second.

6) A solid disc
has a moment of inertia equal to (1/2)MR^{2}. If a disc with a radius
of 0.35 m and a mass of 0.95 kg spins 2.0 times in 0.75 seconds, what is its
angular momentum? Assume it’s spinning clockwise in a horizontal plane, and be
very careful with your units.

7) Take the disc from Problem 6 and decrease its radius by half while it is spinning. If there are no external torques, what is its new angular velocity?

8) A neutron star
forms when the remains of a massive star collapses after a supernova explosion.
Before collapse, the star has a radius of 7 × 10^{8} m. After collapse
it has a radius of 10^{4} m. If the initial angular speed is 7.3 × 10^{-6}
radians/second, what is the angular speed after the collapse? The mass is the
same before and after collapse. Model the rotating star as a uniform sphere – so
its moment of inertia equals (2/5)MR^{2} – and be careful with
precision.

9) Convert the speed found in Problem 8 from radians/second to rotations/second. Again, be careful with precision.

10) Picture a vertical rotational axis. A 0.45 m horizontal lever is perpendicular to the axis, pointed east. Apply a 25 N force, due north. Calculate the torque. Don’t forget the direction.