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?
acp=r x ω2
at= 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 ω2 =R x α I canceled out the R
ω2= α Here I thought that since ω equals 2π/T I could substitute it for ω since it has T for period
(2π/T)2 = α I took the square root of that.
which relates to time
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).