Is the total moment of inertia of an object equal to the moments of inertia of its parts?
Briefly discuss the concept of moment of inertia and the parallel axis theorem on page 281 of the text. Can you think of a body that has the same moment of inertia for all possible axes? If so, give an example. Can you think of a body that has the same moment of inertia for all axes passing through a certain point? If so, give an example and indicate where that point is located.
Young and Freedman 9-37:
A wagon wheel is constructed as shown in figure 9-22 on page 289 of the text. The radius of the wheel is 0.300 m, and the rim has a mass of 1.60 kg. Each of the eight spokes, which lie along a diameter and are 0.300 m long, has a mass of 0.320 kg. What is the moment of inertia of the wheel about an axis through its center and perpendicular to the plane of the wheel? (Use the information in Table 9-2 on p. 278 of the text.)
Two heavy disks are connected by a short rod of much smaller radius. (Picture a dumbbell … not the person beside you … a weightlifter's dumbbell!) The system is placed on a narrow inclined plane so that the disks hang over the sides and the system rolls down the inclined plane on the rod (the part that connects the two weights) without slipping. Near the bottom of the incline the disks touch the horizontal table top and the system takes off with greatly increased translational speed. Explain why this happens.
Young and Freedman 9-71:
A meter stick with a mass of 0.060 kg is pivoted about one end so that it can rotate without friction about a horizontal axis. The meter stick is held in a horizontal position and released. As it swings through the vertical, calculate a) the change in gravitational potential energy that has occurred; b) the angular velocity of the stick; c) the linear velocity of the end of the stick opposite the axis. d) Compare the answer in part (c) to the speed of a particle that has fallen 1.00 m, starting from rest.
In tightening cylinder-head bolts in an automobile engine, the critical quantity is the torque applied to the bolts. Why is this more important than the actual force applied to the wrench handle?
Young and Freedman 10-17:
A string is wrapped several times around the rim of a small hoop of radius 0.0800 m and mass 0.120 kg. If the free end of the string is held in place and the hoop is released from rest (see figure 10-39 on page 321 of the text), calculate a) the tension in the string while the hoop descends as the string unwinds; b) the time it takes the hoop to descend 0.600 m; c) the angular velocity of the rotating hoop after it has descended 0.600 m.
If time permits-
Young and Freedman 10-33:
A small block on a frictionless horizontal surface has a mass of 0.0300 kg. It is attached to a massless cord passing through a hole in the surface (see figure 10-41 on page 322 of text). The block is originally revolving at a distance of 0.200 m from the hole with an angular velocity of 1.75 rad/s. The cord is then pulled from below, shortening the radius of the circle in which the block revolves to 0.100m. The block may be treated as a particle. a) Is the angular momentum conserved? Why or why not? b) What is the new angular velocity? c) Find the change in kinetic energy of the block. d) How much work was done in pulling the cord?