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Chapter 11: Q9Q (page 320)
Figure 11-28 gives the angular momentum magnitude Lof a wheel versustime t. Rank the four-lettered time intervals according to the magnitude
of the torque acting on the wheel, greatest first.
The ranking of time intervals according to the magnitude of torque is
.
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Question: A particle is to move in an xyplane, clockwise around the origin as seen from the positive side of the zaxis. In unit-vector notation, what torque acts on the particle (aIf the magnitude of its angular momentum about the origin is? (b) If the magnitude of its angular momentum about the origin is(b) If the magnitude of its angular momentum about the origin is (d)If the magnitude of its angular momentum about the origin is
A uniform disk of mass and radius can rotate freely about its fixed centre like a merry-go-round. A smaller uniform disk of mass and radius lies on top of the larger disk, concentric with it. Initially the two disks rotate together with an angular velocity of Then a slight disturbance causes the smaller disk to slide outward across the larger disk, until the outer edge of the smaller disk catches on the outer edge of the larger disk. Afterward, the two disks again rotate together (without further sliding).
(a) What then is their angular velocity about the centre of the larger disk?
(b) What is the ratio of the new kinetic energy of the two-disk system to the system鈥檚 initial kinetic energy?
In the instant of Figure, two particles move in an xy plane. Particle P1has mass 6.5kgand speed v1 = 202m/s, and it is at distance d1 = 105mfrom point O. Particle P2has mass 3.1kgand speed v2 = 3.6m/sand it is at distance d2 = 2.8mfrom point O. (a) What is the magnitude of the net angular momentum of the two particles about O? (b) What is the direction of the net angular momentum of the two particles about O?
Non-uniform cylindrical object.InFigure, a cylindrical object of massMand radius Rrolls smoothly from rest down a ramp and onto a horizontal section. From there it rolls off the ramp and onto the floor, landing a horizontal distance d = 0.506m from the end of the ramp. The initial height of the object is H = 0.90m ; the end of the ramp is at height h = 0.10m . The object consists of an outer cylindrical shell (of a certain uniform density) that is glued to a central cylinder (of a different uniform density). The rotational inertia of the object can be expressed in the general form but b is not 0.5as it is for a cylinder of uniform density. Determine .
Two disks are mounted (like a merry-go-round) on low-friction bearings on the same axle and can be brought together so that they couple and rotate as one unit. The first disk, with rotational inertia about its central axis, is set spinning counter clockwise at . The second disk, with rotational inertia about its central axis, is set spinning counter clockwise at They then couple together.
(a) What is their angular speed after coupling? If instead the second disk is set spinning clockwise at 900 rev/min,
(b) what are their angular speed?
(c) What are their direction of rotation after they couple together?
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