Question

An 19-cm-long bicycle crank arm, with a pedal at one end, is attached to a 23-cm-diameter sprocket, the toothed disk around which the chain moves. A cyclist riding this bike increases her pedaling rate from 65 rpm to 90 rpm in 10 s .

Answer 1

The tangential acceleration of the pedal is 0.0301 m/s².

Step-by-step explanation:

Given that,

Length = 19 cm

Diameter = 23 cm

Time = 10 sec

Initial angular velocity = 65 rpm

Final velocity = 90 rpm

Suppose we need to find the tangential acceleration of the pedal

We need to calculate the tangential acceleration of the pedal

Using formula of tangential acceleration

`a_(t)=r\alpha`

`a_(t)=(23*10^(-2))/(2)*(\omega_(2)-\omega_(1))/(t)`

`a_(t)=(23*10^(-2))/(2)*(90*(2]pi)/(60)-65*(2\pi)/(60))/(10)`

`a_(t)=0.0301\ m/s^2`

Hence, The tangential acceleration of the pedal is 0.0301 m/s².