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## Homework Statement

A wheel of radius R starts from rest and accelerates with a constant angular acceleration α about a fixed axis. At what time t will the centripetal and tangential acceleration of a point on the rim have the same magnitude?

## Homework Equations

a

_{cp}=r x ω

^{2}

a

_{t}= r x α

ω= 2π / T → T=2π/ω

## The Attempt at a Solution

The problem states that the centripetal and tangential acceleration will have the same magnitude at time t.

So I listed the equation for centripetal acceleration and tangential acceleration and thought that I can put them equal to each other since the magnitudes are the same.

R x ω

^{2}=R x α I canceled out the R

ω

^{2}= α Here I thought that since ω equals 2π/T I could substitute it for ω since it has T for period

which relates to time

^{2}= α I took the square root of that.

2π/T = √α Solving for T

T = 2π/(√α)

So would this be the time? The AP Physics Book (3rd Edition by James S. Walker doesn't give me a solution since the problem number is even (only gives for odd).