Angular Acceleration| Circular Motion| Physics

Your car tire is rotating at 4.0 rev/s when suddenly you press down hard on the accelerator. After traveling 300 m, the tire’s rotation has increased to 6.5 rev/s . The radius of the tire is 32 cm.

A) What was the tire’s angular acceleration? Give your answer in rad/s²?

SOLUTION:

PART A

ANSWER: α=0.55 rad/s²

We are given an initial angular velocity of 4.0 rev/s and a final angular acceleration of 6.5 rev/s. Convert this angular velocities to rad/s.

\:\frac{4.0\:rev}{s}\times \frac{2\pi \:rad}{1\:rev}=8\pi \:\frac{rad}{s}

\:\frac{6.5\:rev}{s}\times \frac{2\pi \:rad}{1\:rev}=13\pi \:\frac{rad}{s}

The car traveled s=300\:m. Solve for the angular displacement

\theta =\frac{s}{r}=\frac{300\:m}{0.32\:m}=937.5\:rad

Solve for the angular acceleration

\left(\omega _f\right)^2=\left(\omega _i\right)^2+2\alpha \Delta \theta

\left(13\pi \right)^2=\left(8\pi \right)^2+2\alpha \left(937.5\right)

\alpha =0.55\:rad/s^2