What is the equation for moment of inertia?

A rock tied to the end of string swings at a constant angular rate. If you are told that the string can support a total of 85 N of force before breaking, what is the maximum angular velocity the rock can rotate if the rock has a mass of 0.16 kg, and the length of the string is 0.5 m? Give your answer in units of radian per second

A figure skater has a moment of inertia of 0.33 kg-m2.  He is spinning at 336.4 rpm.  He extends his arms until he slows down to 74.3 rpm.  What is his new moment of inerta (in kg-m2)?

A person sits in a chair that is free to rotate without friction. Intheir hands, they hold two masses: Mass m1 = 5.0 kg a distance r1 = 0.35m  from their body and mass m2 = 3.0 kg a distance r2 = 0.75 m from their body. a. What is the moment of inertia of the person and twomasses about a vertical axis that goes through the person? Hint: because of the choice of axis, we can ignore Iperson.

A wheel rotates from rest to 60 rad/s at a rate of 100 rad/s2.What angle did the wheel turn while accelerating?

Two forces act on a uniform disk with a radius of 2.0 cm and a mass of 20.0 g which is initially at rest.  After 1.25 s the disk has an angular velocity of 250 rad/s counterclockwise.  Determine the force F2 if F1 has a magnitude of 0.1 N.  Write your answer to the hundredth newton.

An old vinyl record is played on a turntable that turns at a rate of 45 rotations per minute. Find the angular speed in radians per second. Give your answer as a fraction and do not include units. Keep your answer in terms of π if necessary.

The turntable of the record player has an angular velocity of 625.5 rev/min when it is turned off. It comes to rest  5.3 s after being turned off. What is the angular acceleration of the turntable  in rad/s2 (use 3 significant figures).