An 15-cm-long bicycle crank arm, with a pedal at one end, is attached to a 25-cm-diameter sprocket, the toothed disk around which the chain moves. A cyclist riding this bike increases her pedaling rate from 65 rpm to 91 rpm in 11 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? Need units as well

Any object's rotational motion experiences tangential acceleration, which is the rate at which the tangential velocity varies.
When an object is moving, it behaves in a tangential direction.
When an object is moving in a circle, the tangential velocity also operates in the same direction. Only when an object follows a circular path does tangential acceleration take place.
In cases where the body is rotating more quickly, it is positive; in cases where it is slowing down, it is negative; and in cases where the body is rotating uniformly throughout the orbit, it is zero.

Initial angular velocity, w = 65rpm = 65(rad/s = 6.594rad/s

Final angular velocity, w = 91rpm = 91(rad/s = 9.734rad/s

time taken, t= 11s

Then let total radians covered in this much time be 0 and angular acceleration be a, using equations of motion.

a). 9.734 6.59 and 0.2854rad/s

= (9.734)(6.594) +2(0.2854)/3

A=0.5708

b).Then radius of sprocket R= diameter/2= (25/2)cm E =12.5cm

Then length of chain passes over the top of sprocket in this intervalis

r= (0-12.5m)(89/ 821)

r=9.4m

To study about tangential acceleration -

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