A person is riding a bicycle, and its wheels have an angular velocity of 12.7 ra

Question

A person is riding a bicycle, and its wheels have an angular velocity of 12.7 rad/s. Then, the brakes are applied and the bike is brought to a uniform stop. During braking, the angular displacement of each wheel is 12.4 revolutions. (a) How much time does it take for the bike to come to rest? (b) What is the anguar acceleration (in rad/s2) of each wheel?

Explanation / Answer

(a) Each wheel goes through a radial displacement of: ?? = 18.0rev(2prad/1.00rev) = 113.04 rad The time for the bike to come to rest is: ?? = (?0 + ?)t / 2 t = 2?? / ?0----------------->? = 0, the bike comes to rest = 2(113.04 rad) / 12.4 rad/s = 18.23s (b) The angular acceleration is: ? = ?0 + at a = -?0/t = -12.4rad/s / 18.23s = -.680 rad/s²

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