Torque and Rotational Motion

Which of the following scenarios represents rotational equilibrium?

A system has a net force of zero but a non-zero net torque. Which of the following is true?

A ladder leans against a wall. What conditions must be met for the ladder to be in both translational and rotational equilibrium?

A seesaw has two people of different weights sitting at different distances from the pivot. The seesaw is supported such that it is level (translational equilibrium). If the support is suddenly removed, what will happen?

What happens to the angular velocity of an object if the net torque acting on it is zero?

Three forces act on a beam. Force 1 is 10N at 2m from the pivot, force 2 is 5N at 4m from the pivot in the opposite direction, and force 3 is 2N at the pivot. Is the beam in rotational equilibrium?

A wheel with a moment of inertia of 2 $kg*m^2$ experiences a net torque of 5 Nm. What is its angular acceleration?

A uniform beam of length L and weight W is supported by a pivot at one end and a cable at the other end. The cable makes an angle of $\theta$ with the beam. Determine the tension in the cable in terms of W and $\theta$.

A rotating wheel has a kinetic energy of 100 J. If a torque of 10 Nm is applied to stop the wheel, through what angle does the wheel rotate before coming to rest?

A spinning disk collides with a stationary disk of the same size and mass. If the two disks stick together after the collision, what is their final angular velocity in terms of the initial angular velocity of the first disk?