# Tangential acceleration of a bicycle pedal

• daffy
In summary, the problem involves a cyclist riding a bike with a 17-cm long crank arm attached to a 24-cm diameter sprocket. The cyclist increases her pedaling rate from 64rpm to 95rpm in 12 seconds. The solution involves converting rpm to rad/sec, calculating rotational acceleration and tangential acceleration. The calculated tangential acceleration is approximately 0.046 m/sec2. The correctness of the solution is questioned, but based on the given information, it appears to be correct. The units of the answer were not specified.
daffy
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.

## 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

c. calculate tangential acceleration of the pedal
αt ≈ 0.271 rad/sec2 * 17 cm
αt ≈ 0.271 rad/sec2 * 0.17 m
αt ≈ 0.046 m/sec2

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

Last edited:
Your working all looks correct. You didn't state the actual question, e.g. what units the answer is to be in.

## 1. What is tangential acceleration?

Tangential acceleration is the rate of change of an object's tangential velocity. In simpler terms, it is the acceleration of an object moving in a circular path.

## 2. How does tangential acceleration affect a bicycle pedal?

The tangential acceleration of a bicycle pedal is what causes it to move in a circular motion as the bike moves forward. Without this acceleration, the pedal would simply move in a straight line and not contribute to the motion of the bike.

## 3. What factors affect the tangential acceleration of a bicycle pedal?

The tangential acceleration of a bicycle pedal is affected by the speed of the bike, the radius of the pedal's circular motion, and the force applied by the rider's leg. The greater the speed and force, and the smaller the radius, the greater the tangential acceleration will be.

## 4. How is tangential acceleration calculated?

Tangential acceleration can be calculated using the formula a = v^2 / r, where a is the tangential acceleration, v is the tangential velocity, and r is the radius of the circular motion. This formula can be applied to any object moving in a circular path, including a bicycle pedal.

## 5. Why is understanding tangential acceleration important in cycling?

Understanding tangential acceleration is important in cycling because it allows cyclists to optimize their pedaling technique to increase speed and efficiency. By applying the right amount of force at the right time, cyclists can maximize their tangential acceleration and therefore their overall speed on the bike.

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