An 15-cm-long bicycle crank arm, with a pedal at one end, is attached to a 21-cm-diameter sprocket, the toothed disk around which the chain moves. a cyclist riding this bike increases her pedaling rate from 62 rpm to 95 rpm in 12 s . a) what is the tangential acceleration of the pedal?

b)what length of chain passes over the top of the sprocket during this interval?

Explanation:

It is given that,

Length of the bicycle crank, l = 15 cm = 0.15 m

Diameter of sprocket, d = 21 cm

Radius, r = 0.105 m

Initial angular velocity,

Final angular velocity,

Time, t = 12 s

(a) The relation between the tangential acceleration and the angular acceleration. It is given by :

(b) Using third equation of kinematics as :

Let l is the length of the chain,

l = 10.35 m

Hence, this is the required solution.