# How to calculate angular velocity given constant tangential acceleration? [closed]

A car starts moving in a circle with a radius of $200 \text{ m}$. It has a constant tangential acceleration of $1{\text{m}\over {\text{s}}^{2}}$.

a. What is the angular acceleration?

b. What is the angular velocity of the car $10 \text{ s}$ after it started to drive?

Attempt: a. If the velocity grows by $1 \frac{\text{m}}{\text{s}}$, then it grows by $\frac{1}{2\pi R} \frac{\text{rad}}{\text{s}}$ and I should just convert the radians to degrees?

As for b, I am not sure at all. I am not sure about a. either. I could really use any help or guidance.

## closed as off-topic by John Rennie, Martin, Kyle Kanos, Qmechanic♦Apr 27 '15 at 15:06

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The angular acceleration $\alpha$ is just $\alpha = a/r = 1/200\textrm{rad/s}^2$ where $a$ is the tangential acceleration and $r$ the radius of the circle. Here, we can see that $\alpha$ is constant, which allows us to use the constant acceleration equations in their angular form.
For (b) you can use the angular constant acceleration equations. You have $\alpha$, $t$, and the starting angular velocity $\omega_0=0$. Using $$\omega_f = \omega_0+\alpha t$$ gives $$\omega_f = 0 + {1\over200}\times10= 0.05\textrm{rad/s}$$ For a list of these equations (hopefully they are familiar already but if not...) see http://en.wikipedia.org/wiki/Equations_of_motion#Constant_circular_acceleration