JiTT Exercises

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1			A book measures 3 cm by 16 cm by 24 cm. About which of the axes shown in Fig. 8.44 is its rotational inertia smallest? Fig. 8.44




2			Figure 8.49 shows a common balancing toy with weights extending on either side. The toy is extremely stable. It can be pushed quite far off center one way or the other but it does not fall over. Explain why it is so stable. Fig. 8.49




3			The CG of the upper body of a bird is located below the hips; in a human, the CG of the upper body is located well above the hips (see Fig. 8.51). Since the upper body is supported by the hips, are birds or humans more stable? Consider what happens if the upper body is displaced a little so that its CG is not directly above or below the hips. In what direction does the torque due to gravity tend to make the upper body rotate about an axis through the hips? Fig. 8.51




4			A child of mass 40.0 kg is sitting on a horizontal seesaw at a distance of 2.0 m from the supporting axis. What is the magnitude of the torque about the axis due to the weight of the child?




5			A tower outside the Houses of Parliament in London has a famous clock commonly referred to as Big Ben, the name of its 13-ton chiming bell. The hour hand of each clock face is 2.7 m long and has a mass of 60.0 kg. Assume the hour hand to be a uniform rod attached at one end. (a) What is the torque on the clock mechanism due to the weight of one of the four hour hands when the clock strikes noon? The axis of rotation is perpendicular to a clock face and through the center of the clock. (b) What is the torque due to the weight of one hour hand about the same axis when the clock tolls 9:00 A.M.?




6			A flywheel of mass 182 kg has an effective radius of 0.62 m (assume the mass is concentrated along a circumference located at the effective radius of the flywheel). (a) What torque is required to bring this wheel from rest to a speed of 120 rpm in a time interval of 30.0 s? (b) How much work is done during the 30.0 s?




7			A rod being used as a lever is shown in Fig. 8.61. The fulcrum is 1.2 m from the load and 2.4 m from the applied force. If the load has a mass of 20.0 kg, what force must be applied to lift the load? Fig. 8.61




8			A spinning flywheel has rotational inertia I = 400.0 kg·m². Its angular velocity decreases from 20.0 rad/s to zero in 300.0 s due to friction. What is the frictional torque acting?




9			Assume the Earth is a uniform solid sphere with radius of 6.37 × 10⁶ m and mass of 5.98 × 10²⁴ kg. Find the magnitude of the angular momentum of the Earth due to rotation about its axis.




10			A skater is initially spinning at a rate of 10.0 rad/s with a rotational inertia of 2.50 kg·m² when her arms are extended. What is her angular velocity after she pulls her arms in and reduces her rotational inertia to 1.60 kg·m²?

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