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Question: An automobile traveling 30 mi/hr has wheels 28 inches in diameter. If

ID: 2016207 • Letter: Q

Question

Question: An automobile traveling 30 mi/hr has wheels 28 inches in diameter. If the car is brought to a stop uniformly in 78 turns of the wheels, what is the magnitude of the angular acceleration of the wheels (in radians/second^2)?

As far as the concept goes, I am looking for the angular acceleration, so what I did to make my way toward that was to set velocity of center mass (automobile's speed) equal to radius * angular velocity:
vcm = r

and I solved for which gives me the value of angular velocity (note, that I took units into consideration). I do not know where to go from there. I tried to plug in the values for the period formula T=2r/v but I do not know if I'm on the right track.

Would highly appreciate a walkthrough. Thanks!

Explanation / Answer

Data: Initial velocity, v1 = 30 mi/hr                            = 30 * 0.447 m/s                            = 13.41 m/s Diameter, D = 28 inches Radius, r = 14 inches                = 14 * 0.0254 m                = 0.3556 m No. of turns, n = 78 turns Solution: Initial angular speed, 1 = v1 / r                                       = 13.41 / 0.3556                                       = 37.71 rad/s Final angular speed, 2 = 0 rad/s Angular displacement, = 2n                                      = 2 * 78 rad                                      = 490.1 rad Angular acceleation, = [ 2^2 - 1^2 ] / 2                                    = [ 0 - 37.71^2 ] / ( 2 * 490.1 )                                    = - 1.45 rad/s^2 Ans: Angular acceleration, = - 1.45 rad/s^2
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