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rolling motions and torque acting on a CD

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Please see attached problems.

1. An automobile tire has a radius of 0.370 m, and its center moves forward with a linear speed of v = 16.0 m/s.
(a) Determine the angular speed of the wheel. (Assume that there is no slipping of the surfaces in contact during the rolling motion.)
(b) Relative to the axle, what is the tangential speed of a point located 0.175 m from the axle?

2. A uniform plank of length 4.8 m and weight 227 N rests horizontally on two supports, with 1.1 m of the plank hanging over the right support (see the drawing). To what distance x can a person who weighs 449 N walk on the overhanging part of the plank before it just begins to tip?

3. A CD has a mass of 17 g and a radius of 6.0 cm. When inserted into a player, the CD starts from rest and accelerates to an angular velocity of 18 rad/s in 0.84 s. Assuming the CD is a uniform solid disk, determine the net torque acting on it.

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Solution Summary

The solution shows the relationship among the linear velocity, angular velocity, and tangential speed in a rolling motion of an automobile tire. It also shows how to calculate the net torque acting on a CD.

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Please see the attached file for detailed solution.

1. (a) The angular speed omega = v /r = 16.0 / 0.370 = 43.2 rad/s
(b) All points on the wheel have the same ...

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