An 20-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 63 rpm to 94 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?

To solve the problem, it is necessary to apply the concepts related to the kinematic equations of the description of angular movement.

The angular velocity can be described as

Where,

Final Angular Velocity

Initial Angular velocity

Angular acceleration

t = time

The relation between the tangential acceleration is given as,

where,

r = radius.

PART A ) Using our values and replacing at the previous equation we have that

Replacing the previous equation with our values we have,

The tangential velocity then would be,

Part B) To find the displacement as a function of angular velocity and angular acceleration regardless of time, we would use the equation

Replacing with our values and re-arrange to find

That is equal in revolution to

The linear displacement of the system is,

the answer would be c