A solid uniform disk of mass 21.0 kg and radius 85.0 cm is at rest flat on a frictionless surface. Figure 10–76 shows a view from above. A string is wrapped around the rim of the disk and a constant force of 35.0 N is applied to the string. The string does not slip on the rim. In what direction does the cm move?

A ball rolling on a circular track, starting from rest, has angular acceleration $\alpha$. Find an expression, in terms of $\alpha$, for the time at which the ball's acceleration vector a is ${45}^{\circ }$ away from a radial line toward the center of the circle.

Let us treat a helicopter rotor blade as a long thin rod, as shown in Fig. 10–60. If each of the three rotor helicopter blades is 3.75 m long and has a mass of 135 kg, calculate the moment of inertia of the three rotor blades about the axis of rotation.

A bowling ball of mass 7.3 kg and radius 9.0 cm rolls without slipping down a lane at 3.7 m/s. Calculate its total kinetic energy.

A 2.20-kg hoop 1.20 m in diameter is rolling to the right without slipping on a horizontal floor at a steady 2.60 rad/s. Find the velocity vector for each of the points in part (c), but this time as viewed by someone moving along with the same velocity as the hoop.

A long, light rope is wrapped around a cylinder of radius 40 cm, which is at rest on a flat surface, free to move. You pull horizontally on the rope, so it unwinds at the top of the cylinder, causing it to begin to roll without slipping. You keep pulling until the cylinder reaches 10 RPM. Calculate the speed of the rope at the instant the cylinder reaches 10 RPM.

A ball rolling on a circular track, starting from rest, has angular acceleration $\alpha$. Find an expression, in terms of $\alpha$, for the time at which the ball's acceleration vector a is ${45}^{\circ }$ away from a radial line toward the center of the circle.