A composite disc is made out of two concentric cylinders, as shown. The inner cylinder has radius 30 cm. The outer cylinder has radius 50 cm. If you pull on a light rope attached to the edge of the outer cylinder (shown left) with 100 N, how hard must you pull on a light rope attached to the edge of the inner cylinder (shown right) so the disc does not spin?

A pole projects horizontally from the front wall of a shop. A 6.1-kg sign hangs from the pole at a point 2.2 m from the wall (Fig. 12–88).

(b) If the pole is not to fall off, there must be another torque exerted to balance it. What exerts this torque? Use a diagram to show how this torque must act.

<IMAGE>

A pole projects horizontally from the front wall of a shop. A 6.1-kg sign hangs from the pole at a point 2.2 m from the wall (Fig. 12–88).

(a) What is the torque due to this sign calculated about the point where the pole meets the wall?

<IMAGE>

If 25 kg is the maximum mass m that a person can hold in a hand when the arm is positioned with a 105° angle at the elbow as shown in Fig. 12–102, what is the maximum force Fₘₐₓ that the biceps muscle exerts on the forearm? Assume the forearm and hand have a total mass of 2.0 kg with a cg that is 15 cm from the elbow, and that the biceps muscle attaches 5.0 cm from the elbow.

<IMAGE>

A woman holds a 1.8-m-long uniform 10.0-kg pole as shown in Fig. 12–84.

(a) Determine the forces she must exert with each hand (magnitude and direction). To what position should she move her left hand so that neither hand has to exert a force greater than (b) 150 N? (c) 85 N?

<IMAGE>