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daffy

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I'm attempting to solve a mastering physics problem, but I've seem to run into a dead-end on this problem. I've worked out my solution and I'm certain I've rounded my sig figs correctly, but mp doesn't accept the answer.

An 17-cm long bicycle crank arm, with a pedal at one end, is attached to a 24-cm diameter sprocket, the toothed disk around which the chain moves. A cyclist riding this bike increases her pedaling rate from 64rpm to 95rpm in 12 seconds.

α tangential = αt = α * radius

α = dω/dt

a. put terms in rpm into rad/sec

ωi = 64 rpm

ωf = 95 rpm

ωi = 64 (1 rotation / 1 minute) * (2∏ rad / 1 rotation) * (1 minute / 60 sec) ≈ 6.702 rad/sec

ωf = 95 (1 rotation / 1 minute) * (2∏ rad / 1 rotation) * (1 minute / 60 sec) ≈ 9.948 rad/sec

b. calculate rotational acceleration

α = (ωf - ωi) / time difference

α = (ωf - ωi) / 12 sec

α ≈ 0.271 rad/sec

c. calculate tangential acceleration of the pedal

αt = α * radius

αt ≈ 0.271 rad/sec

αt ≈ 0.271 rad/sec

αt ≈ 0.046 m/sec

Does anybody know what I'm doing wrong in my reasoning? Or am I not understanding the mechanics of a bicycle correctly?

Thanks in advance

## Homework Statement

An 17-cm long bicycle crank arm, with a pedal at one end, is attached to a 24-cm diameter sprocket, the toothed disk around which the chain moves. A cyclist riding this bike increases her pedaling rate from 64rpm to 95rpm in 12 seconds.

## Homework Equations

α tangential = αt = α * radius

α = dω/dt

## The Attempt at a Solution

a. put terms in rpm into rad/sec

ωi = 64 rpm

ωf = 95 rpm

ωi = 64 (1 rotation / 1 minute) * (2∏ rad / 1 rotation) * (1 minute / 60 sec) ≈ 6.702 rad/sec

ωf = 95 (1 rotation / 1 minute) * (2∏ rad / 1 rotation) * (1 minute / 60 sec) ≈ 9.948 rad/sec

b. calculate rotational acceleration

α = (ωf - ωi) / time difference

α = (ωf - ωi) / 12 sec

α ≈ 0.271 rad/sec

^{2}c. calculate tangential acceleration of the pedal

αt = α * radius

αt ≈ 0.271 rad/sec

^{2}* 17 cmαt ≈ 0.271 rad/sec

^{2}* 0.17 mαt ≈ 0.046 m/sec

^{2}Does anybody know what I'm doing wrong in my reasoning? Or am I not understanding the mechanics of a bicycle correctly?

Thanks in advance

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