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Chapter 10: Q7Q (page 286)
Figure 10-25ais an overhead view of a horizontal bar that can pivot; two horizontal forces act on the bar, but it is stationary. If the angle between the bar and is now decreased from and the bar is still not to turn, should be made larger, made smaller, or left the same?
The force will increase.
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In Fig. , block has mass , block has mass , and the pulley, which is mounted on a horizontal axle with negligible friction, has radius . When released from rest, block falls in without the cord slipping on the pulley. (a) What is the magnitude of the acceleration of the blocks? What are (b) tension and (c) tension ? (d) What is the magnitude of the pulley’s angular acceleration? (e) What is its rotational inertia?
(a) Show that the rotational inertia of a solid cylinder of mass M and radius R about its central axis is equal to the rotational inertia of a thin hoop of mass M and radius about its central axis. (b) Show that the rotational inertia I of any given body of mass M about any given axis is equal to the rotational inertia of an equivalent hoop about that axis, if the hoop has the same mass M and a radius k given by The radius k of the equivalent hoop is called the radius of gyration of the given body.
Figure 10 - 27shows three flat disks (of the same radius) that can rotate about their centers like merry-go-rounds. Each disk consists of the same two materials, one denser than the other (density is mass per unit volume). In disks 1and 3, the denser material forms the outer half of the disk area. In disk 2, it forms the inner half of the disk area. Forces with identical magnitudes are applied tangentially to the disk, either at the outer edge or at the interface of the two materials, as shown. Rank the disks according to (a) the torque about the disk center, (b) the rotational inertia about the disk center, and (c) the angular acceleration of the disk, greatest first.
In Fig., a wheel of radius is mounted on a frictionless horizontal axle. A massless cord is wrapped around the wheel and attached to abox that slides on a frictionless surface inclined at angle with the horizontal. The box accelerates down the surface at. What is the rotational inertia of the wheel about the axle?
A small ball with massis mounted on one end of a rod long and of negligible mass. The system rotates in a horizontal circle about the other end of the rod at .
(a) Calculate the rotational inertia of the system about the axis of rotation.
(b) There is an air drag of on the ball, directed opposite its motion. What torque must be applied to the system to keep it rotating at constant speed?
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