Find the linear acceleration of the bicycle.?

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hevessels1219

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A bicycle has wheels with a diameter of .580 m. It accelerates uniformly and the rate of rotation of its wheels increases from 223 rpm to 280 rpm in at time of 17.9 s. Find the linear acceleration of the bicycle.
 
First, we need to convert the change in rpm into radians per second:

( 37 rev / min ) ( 2π radians / rev ) ( 1 min / 60 sec ) = 3.9 radians / sec

The angular acceleration of the bicycle is then

α = ( 3.9 radians / sec ) / ( 17.9 sec ) = .22 radians / s²

Then the linear accelaration is

a = rα = ( .290 m ) ( .22 radians / s² ) = .06 m/s²
 
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