Answered: Consider a bowling ball which is tossed…

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Consider a bowling ball which is tossed down a bowling alley. For this problem, we will consider the bowling ball to be a uniform sphere of mass M and radius R, with a moment of inertia given by I = (2/5)MR2. The moment the ball hits the ground (t = 0), it is moving horizontally with initial linear speed v0, but not rotating (ω0 = 0). Due to kinetic friction between the ground and the ball, it begins to rotate as it slides. The coefficient of kinetic friction is µk. As the ball slides along the lane, its angular speed steadily increases. At some point (time tc), the“no-slip” condition kicks in, so that ω = v/R. After this, the ball moves with a constant linear and

angular speed. Solve all parts of this problem symbolically.

1. Use Newton’s second law to find an expression for the linear acceleration of the ball along the x-direction before the no-slip condition kicks in, ax. The free body diagram of the ball is shown below. Your final expression should only involve the variables g

and µk.

2.Use the rotational version of Newton’s second law to find an expression for the angular acceleration of the ball along the z-direction before the no-slip condition kicks in, αz. Your final expression should only involve the variables R, g, and µk.

Definition Definition Rate of change of angular velocity. Angular acceleration indicates how fast the angular velocity changes over time. It is a vector quantity and has both magnitude and direction. Magnitude is represented by the length of the vector and direction is represented by the right-hand thumb rule. An angular acceleration vector will be always perpendicular to the plane of rotation. Angular acceleration is generally denoted by the Greek letter α and its SI unit is rad/s 2 .

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