An 19.2-cm-long bicycle crank arm, with a pedal at one end is attached to a 20.6-cm-diameter sprocket, the toothed disk around which the chain moves. A cyclist riding this bike increases her pedaling rate from 57 rpm to 86 rpm in 10.7 s. What is the tangential acceleration of the pedal?

0.0545 m/s2

Explanation:

19.2 cm = 0.192 m

We can convert rpm (revolution per minute) to angular velocity rad/s knowing that each revolution is 2π rad and each minute is 60 seconds.

57 rpm = 57 * 2π / 60 = 6 rad/s

86 rpm = 86 * 2π / 60 = 9 rad/s

The angular acceleration of the sprocket is the change in angular velocity per unit of time

The tangential acceleration of the pedal is the product of its angular acceleration and the radius of rotation, aka the pedal arm length L = 0.192 m

Tangential acceleration==0.029233 m/s^2

Explanation

tangential acceleration=

=ω/t

alpha=2((86/60)-(57/60))/10.7

=0.2838 m/s^2

at=*r

radius=d/2=20.6/2=10.3 cm=0.103 m

at=0.2838*0.103=0.029233 m/s^2