Given: The disk of radius R rolls without slipping on a horizontal surface with

Question

Given: The disk of radius R rolls without slipping on a horizontal surface with the speed and acceleration of the disk center O given by vo and ao, respectively. A particle P slides within a semi-circular slot cut in the disk, P moves with a speed of u relative to the disk and a rate of change of speed of ù relative to the disk. The radius of the slot is r. R O Part A: The angular velocity associated with the moving reference frame is: R+r Part B: The angular acceleration a associated with the moving reference frame is (b) 0k (c) a = a (d) a=-aok

Explanation / Answer

Part A: - Angular velocity with respect to moving frame will be

omega = linear velocity/ radius of rotation

= Vo/ R and its direction is outward normal to the page

= Vo/ R k^

Part B : - angular acceleration = omega/ radius of curvature

= omega / R k^ ( so option A is the correct choice).

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