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

Magnitude of angular acceleration = -3.95 rad/s²

Step-by-step explanation:

Angular acceleration is the ratio of linear acceleration and radius.

That is

`\texttt{Angular acceleration}=\frac{\texttt{Linear acceleration}}{\texttt{Radius}}\\\\\alpha =(a)/(r)`

Radius = 72 cm = 0.72 m

Linear acceleration is rate of change of velocity.

`a=(11.7-26.5)/(5.2)=-2.85m/s^2`

Angular acceleration

`\alpha =(a)/(r)=(-2.85)/(0.72)=-3.95rad/s^2`

Angular acceleration = -3.95 rad/s²

Magnitude = 3.95 rad/s²