The angular frequency of a rotating rigid body increases from 500 to 1500 rev/min in 120 s (a) What is the initial angular frequency? (b) What is the initial angular velocity? (c) What is the angular acceleration of the body? (d) Through what angle does it turn in this 120 s? For this question record the answer for (a)-(c). Initial angular frequency fo = [Select] Initial angular velocity wo = [Select] Angular acceleration of the body a = [Select]

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Solution (a) Find the angular displacement after 2.00 s, in both radians and revolutions. 1 A0 = w;t + Use Equation 7.8, setting @; 1.60 rad/s, a = 3.50 rad/s2, and t = 2.00 s. 1 Að = (1.60 rad/s) (2.00 s) + (3.50 rad/s²) (2.00 s)² 2 A0 = 10.2 rad Convert radians to revolutions. A0 = (Am rad)(1.00 rev/2r rad) AO = 16.02 X rev Your response differs from the correct answer by more than 100%. (b) What is the angular speed of the wheel at t = 2.00 s? Substitute the same values into Equation 7.7. @ = @; + at = 1.60 rad/s + (3.50 rad/s²)(2.00 s) W = rad/s Remarks The result of part (b) could also be obtained from Equation 7.9 and the results from part (a). - IN

For rolling without slip, the acceration of a circular disk on an incline plane a=r(alpha) where alpha = to the angular accleration. Qn. What is the difference in acceleration with slipping vs without slipping? Also, why is there no centripetal acceleration (towards the centroid of disk) when the disk is rolling without slippage?