Question

An 18-cm-long bicycle crank arm, with a pedal at one end, is attached to a 20-cm-diameter sprocket, the toothed disk around which the chain moves. A cyclist riding this bike increases her pedaling rate from 60 rpm to 90 rpm in 10 s. a. What is the tangential acceleration of the pedal?

Answer 1

`a_t=0.0565\ rad/s^2`

Step-by-step explanation:

It is given that,

Length of the bicycle crank arm, l = 18 cm = 0.18 m

Its length will act as the radius of arm.

The diameter of the sprocket, d = 20 cm = 0.2 m

A cyclist riding this bike increases her pedaling rate from 60 rpm to 90 rpm in 10 s.

To find,

The tangential acceleration of the pedal.

Solution,

The rate of change of angular displacement is called angular acceleration of the object. It is given by :

`\alpha =(d\omega)/(dt)`

`\alpha =((90-60)\ rpm)/(10\ s)`

`\alpha =(30\ rpm)/(10\ s)`

`\alpha =(3.14\ rad/s)/(10\ s)`

`\alpha =0.314\ rad/s^2`

The relationship between the angular acceleration and the tangential acceleration is given by :

`a_t=r* \alpha`

`a_t=0.18* 0.314`

`a_t=0.0565\ rad/s^2`

Therefore, the tangential acceleration of the pedal is
`0.0565\ rad/s^2`