agcom22ms=−μ021 9821...bgchwhere the minus sign indicates that the center of mass acceleration points left, opposite to its velocity, so that the ball is decelerating. (c) Measured about the center of mass, the torque exerted on the ball due to the frictional force is given by τmgR. Using Table 10-2(f) for the rotational inertia, the angular acceleration becomes (using Eq. 10-45) ()2225 0.21 9.8 m/s547 rad s2522 0.11 mmgRgImRRτμα−−−=====−where the minus sign indicates that the angular acceleration is clockwise, the same direction as ω(so its angular motion is “speeding up’’). (d) The center-of-mass of the sliding ball decelerates from vcom,0to vcomduring time taccording to Eq. 2-11: vvgtcomcom,0. During this time, the angular speed of the ball increases (in magnitude) from zero to according to Eq. 10-12: ωα=tgtRvR52comwhere we have made use of our part (a) result in the last equality. We have two equations involvingvcom, so we eliminate that variable and find
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