A64 (10.3) My 1989 Saab had tires with a diameter of approximately 622 mm. (a) I

Question

A64 (10.3) My 1989 Saab had tires with a diameter of approximately 622 mm. (a) If I was driving at 55 mph (88.5 km/h), determine the angular speed of the tires about their axles. (b) Let's say that I bring the car to rest (under constant acceleration) in 30.0 complete turns of the tires and there is no skidding. What would be the magnitude of the constant angular acceleration of the wheels? (c) How far would the car actually move while I am braking? Answers: (a) 39.5 rad/s, (b) 4.14 rad/s2, (c) 58.6 m

Explanation / Answer

diameter,d=0.622 m ; velocity,v=88.5km/h or 24.5833 m/s ; Turns,n =30

a) Using pure rolling condition, v=wR , w= 24.5833/.311 = 79.0459 rad/s

b) Using (w_final)^2 - (w_initial)^2 = 2 * Alpha* Theta ; 0-6248.2543 = - 2*Alpha* 30*2*pi

Therefore, Alpha=16.5740 rad/s^2

c) linear distance = 30*2*pi*R = 58.622 m

FOR THE GIVEN ANSWERS, THE VALUE GIVEN FOR DIAMETER SHOULD BE THE RADIUS OF THE TIRE

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