torque and acceleration

1) The rotational equivalent of force is _______________________ .

2) The rotational equivalent of mass is _______________________ .

3) If you were standing on a spinning disc
accelerating at 1.2 rad/s^{2}, and you were standing 1.5 m from its
rotational axis, what would be the magnitude of your tangential acceleration?

4) How much torque is needed to make a 9.5 kgm^{2}
object accelerate at 4.2 rad/s^{2}?

5) If you applied a 37 Nm torque to an object and
found its acceleration to be 1.8 rad/s^{2}, what is the object’s moment
of inertia?

6) A 4.5 kg sphere with a 0.25 m radius is
spinning at 7.5 rad/s. How much torque is needed to bring it to a stop in 1.5
seconds? The moment of inertia for a solid sphere is (2/5)MR^{2}.

7) How much force, applied perpendicular to the radius, is needed to bring the sphere from Question 6 from 7.5 rad/s to a stop in 1.5 seconds?

8) A tangential force of 75 N is applied to the
edge of a 3.0 kg disc initially at rest. The radius of the disc is 0.35 m, and
the equation for its moment of inertia is (1/2)MR^{2}. Find angular
acceleration, then calculate the angular speed after the disc has spun two full
rotations.

9) The moment of inertia for a hollow sphere is
(2/3)MR^{2}. Take a 5.5 kg sphere and apply a 25 N force to its 2.5 m
radius. If it starts at rest, how many radians will it spin in 18 seconds?