Question

A car is travelling at a constant speed of 26.5 m/s. Its tires have a radius of 72 cm. If the car slows down at a constant rate to 11.7 m/s over 5.2 s, what is the magnitude of the angular acceleration of the tires during that time? (in rad/s^2)

Answer 1

Answer:

Magnitude of angular acceleration = -3.95 rad/s²

Explanation:

Angular acceleration is the ratio of linear acceleration and radius.

That is

        $\texttt{Angular acceleration}=\frac{\texttt{Linear acceleration}}{\texttt{Radius}}\\\\\alpha =\frac{a}{r}$

Radius = 72 cm = 0.72 m

Linear acceleration is rate of change of velocity.

$a=\frac{11.7-26.5}{5.2}=-2.85m/s^2$

Angular acceleration

        $\alpha =\frac{a}{r}=\frac{-2.85}{0.72}=-3.95rad/s^2$

Angular acceleration = -3.95 rad/s²  

Magnitude =  3.95 rad/s²