Torque and Rotational Dynamics

A rotating object has a rotational inertia of 2 $kg \cdot m^2$. If a net torque of 10 $N \cdot m$ is applied, what is the resulting angular acceleration?

A 10 N force is applied 0.5 m from the axis of rotation at an angle of 30 degrees relative to the radial line. What is the magnitude of the torque?

A wheel rolls down an incline without slipping. How is its linear acceleration related to its angular acceleration?

If the net torque on an object is doubled, what happens to the angular acceleration, assuming rotational inertia remains constant?

Two forces are applied to a rod that is free to rotate about one end. Force $F_1$ = 10 N is applied at the midpoint of the rod, perpendicular to the rod. Force $F_2$ = 5 N is applied at the free end of the rod, also perpendicular to the rod, but in the opposite direction. If the rod is 2 m long, what is the net torque ...

At what angle between the force and the lever arm is the torque maximized?

A solid disk and a hoop have the same mass and radius. If the same torque is applied to both, which will have a greater angular acceleration?

A wheel is rotating with a constant angular velocity. Which of the following statements must be true?

A wheel with a rotational inertia of 5 $kg \cdot m^2$ experiences a torque of 20 $N \cdot m$. What is its angular acceleration?

Two forces are applied to a disk. One force of 5 N is applied at the edge (radius = 0.2 m), and another force of 3 N is applied halfway to the center, in the opposite direction. Calculate the net torque.