A person is riding a bicycle, & its wheels have an angularvelocity of + 20 rad/s

Question

A person is riding a bicycle, & its wheels have an angularvelocity of + 20 rad/s. Then the brakes are applied & the bikeis brought to a uniform stop. During the braking, the angulardisplacement of each wheel is + 15.92 revolution. a) how much time does it take for the bike to come torest? b) what is the angular acceleration (in rad/s2) of eachwheel? book answers: a) 10 s b) - 2.0 rad/s2 Thanks. A person is riding a bicycle, & its wheels have an angularvelocity of + 20 rad/s. Then the brakes are applied & the bikeis brought to a uniform stop. During the braking, the angulardisplacement of each wheel is + 15.92 revolution. a) how much time does it take for the bike to come torest? b) what is the angular acceleration (in rad/s2) of eachwheel? book answers: a) 10 s b) - 2.0 rad/s2 Thanks.

Explanation / Answer

    initial angular velocity, o =20 rad / s     final angular velocity, = 0 rad / s     angular displacement, = 15.92 revolutions= 15.92 * 2 rad = 100.1 rad     (a)        Angular displacement , = [ (o + ) / 2 ] t                                 100.1 = 10 t                                        t = 10 s     (b)     angular acceleration, = ( -o ) / t                                       = - 20 / 10 = - 2 rad / s2

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