The wheels of a motor vehicle are 1 meter in diameter over the tyres. Assuming that no slip takes place between the wheels and the road surface calculate the angular velocity of the wheels when the vehicle is travelling at speed 90km/hr.

The angular velocity of the wheels is 50 rad/s.

To calculate the angular velocity of the wheels, we first need to relate the vehicle's linear speed to the wheel's rotational speed. Here's a step-by-step approach:

Convert the linear speed from km/hr to m/s:
$90 \text{ km/hr} = 90 \times \frac{1000 \text{ m}}{1 \text{ km}} \times \frac{1 \text{ hr}}{3600 \text{ s}} = 25 \text{ m/s}$
Relate the linear speed to the angular speed:
The relationship between linear speed $v$ and angular velocity $\omega$ is:
$v = r \times \omega$
where $r$ is the radius of the wheels. Given that the diameter of the wheels is 1 meter, the radius $r$ is 0.5 meters.
Solve for the angular velocity $\omega$ :
$\omega = \frac{v}{r} = \frac{25 \text{ m/s}}{0.5 \text{ m}} = 50 \text{ rad/s}$

So, the angular velocity of the wheels is $50 \text{ rad/s}$ .

You can verify this result with this online converter from km/h to rad/s