1.) A wheel rotates about a fixed axis with an initial angular velocity of 96 ra

Question

1.) A wheel rotates about a fixed axis with an initial angular velocity of 96 rad/s. During a 2s interval the angular velocity increases to 134 rad/s. How many revolutions does the wheel turn through during this time interval? Assume the angular acceleration was constant during this time interval. Answer in units of rev

2.) A ball of mass m and radius R is both sliding and spinning on a horizontal surface so that its rotational kinetic energy equals its translational kinetic energy. What is the ratio of the ball

Explanation / Answer

a). theta = w *t + 1/2 (angular acceleration) t^2

=> theta = 96 *2 + 1/2 * (134-96)/2 *2^2

=> theta = 230 radians

in units of revolution, theta = 230/2*3.14 = 36.624 rev

b). 1/2 I* w^2 = 1/2 mv^2

=> (0.54mR^2) w^2 = mv^2

=> v/wr = 0.735

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