A rider in a road bike race had an average linear speed of 4

A rider in a road bike race had an average linear speed of 40.479 km/hr. The wheel of him bicycle had a diameter of 45 cm. What is his angular speed, in revolutions per hour?

Solution

Here rule is that

angular velocity= linear velocity x radius

Now as radius here is 45/2 cm =22.5 cm

so its angular velocity = 40.679 x 22.5 =915.28 km per hour.

Now as the circumference of the wheel= total distance covered in one revolution= 2 x 3.14 x RADIUS of wheel

= 2 x 3.14 x 22.5 = 141.3 cm = 141 x 0.00001 km. = 0.001413 km

Now as 0.001413 km covered in 1 revolution

so 1 km is covered in 1/0.001413 revolutions

and 915.28 km is covered in 915.28/0.001413 = 647756.54

So required angular speed = 647757 revolutions per hour.

Answer