Chapter 11
1. (p.298 prob.55) A boy rolls a tire along a straight level street. The tire has mass 9.0kg, radius 0.32m and moment of inertia about its central axis of symmetry of 0.83kg·m2. The boy shoves the tire away from him at a speed of 2.1m/s and sees that the tire leans 10° to the right (Fig. 11-32). (a) How will the gravitational torque affect the subsequent motion of the tire? (b) compare the change in angular momentum caused by this torque in 0.20s to the original magnitude of angular momentum.
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2. (p.299 prob.59) A thin uniform stick of mass M and length l is positioned vertically, with its tip on a frctionless table. It is released and allowed to slip and fall (Fig. 11-35). Determine the speed of its center of mass just before it hits the table.
3. (p.299 prob.62) A baseball bat has a "sweet spot "where a ball can be hit with almost effortless transmission of energy. A careful analysis of baseball dynamics shows that this special spot is located at the point where an applied force would result in pure rotation of the bat about the handle. Determine the location of the sweet spot of the bat shown in Fig. 11-37. The linear mass density of the bat is given roughly by (0.56 + 3.5x)kg/m, where x is in meters measured from the end of the handle. The entire bat is 0.84m long. The desired rotation point should be 5.0cm from the end where the bat is held. [Hint: where is the CM of the bat?]