# Angular Velocity and Acceleration

## Homework Statement

If a bike wheel rotates 9.4 times while slowing down to a stop from an initial angular velocity of 8.1 rad/s, what is the magnitude of the angular acceleration in rad/s/s

## Homework Equations

α = at / r
α = ω / t
α = Θ / t^2
ω = Θ / t
ω = v / r
Θ = ω t + 0.5 α t^2
v final = v initial + at → ω final = ω initial + αt
some of these formulas may be useless, and there possibly are some others not mentioned that i do not know :/

## The Attempt at a Solution

Knowing the initial angular velocity is 8.1 and the final is 0 since the wheel stops, i used
ω final = ω initial + αt
0 = 8.1 + αt
it spins 9.4 times in the time frame during which it slows down, but the radius of the wheel is not given. And i do not know which ω to use in the equation ω = Θ / t in order to find time. If i could get time, then i could use the equation α = ω / t or α = Θ / t^2. Am i even approaching this correctly? if not can somebody point me in the right direction?

BvU
Homework Helper
Hi,

There is another SUVAT equation you need to translate into uniformly decelerated angular motion: ##s = s_0 + v_0 t + {1\over 2} at^2##.

##\theta## takes the place of s (and one revolution is ##2\pi##) to give you a second equation. That way you have 2 eqns for ##\alpha## and ##t##, so you should be able to solve.

Hi,

There is another SUVAT equation you need to translate into uniformly decelerated angular motion: ##s = s_0 + v_0 t + {1\over 2} at^2##.

##\theta## takes the place of s (and one revolution is ##2\pi##) to give you a second equation. That way you have 2 eqns for ##\alpha## and ##t##, so you should be able to solve.
i am still confused as to what two equations these are, if you could provide them for me or hint at what they would be i would greatly appreciate it. I am unsure of what s0 would be, i understand that theta substitutes for s, but it couldn't be for both sides. Is 2pi x 9.4 supposed to be s?

BvU
$$\theta(t) = \theta_0 + \omega_0 t + {1\over 2} \alpha t^2$$ it's that simple (for constant angular acceleration/deceleration -- then ##\alpha < 0##).