Question

A bus has wheels which are 112cm in diameter. How many complete revolutions does each wheel of the bus make in 20 minutes, when the bus is travelling at a speed of 66 km/h?

Answer 1

Hint: Calculate the distance covered in one revolution of the wheel. Hence calculate the total number of revolutions equivalent to 66kms. This will give the number of revolutions per hour. Hence calculate the number of revolutions in 20 mins. Alternatively, calculate the angular velocity of the wheel and hence the number of revolutions in 20mins.

Complete step-by-step answer:
The wheel covers a distance equal to the length of the circumference of the wheel in one revolution.
Given the diameter of the wheel = 112 cm =1.12 m
Hence the radius of the wheel = 0.56m.
Hence distance covered in one revolution $ =2\pi \left( 0.56 \right)=1.12\pi $ .
Hence the number of revolutions in 1 hour $ =\dfrac{66\times 1000}{1.12\pi }=\dfrac{66000\times 7}{1.12\times 22}=\dfrac{21000}{1.12}=18750 $ revolutions.
Hence the number of revolutions in 60 mins = 18750
Hence the number of revolutions in 1 min $ =\dfrac{18750}{60}=312.5 $
Hence the number of revolutions in 20 mins $ =312.5\times 20=6250 $
Hence the number of revolutions made by the wheel of the bus in 20 minutes = 6250

Note: The speed at the circumference of the wheel = 66km/h $ =\dfrac{66\times 1000}{60}\text{m/min=} $ 1100 m/min.
We know that angular velocity $ =\dfrac{\text{Velocity at point P}}{\text{Distance of point P from centre}} $
Hence, we have
Angular velocity $ =\dfrac{1100}{0.56}\text{rad}/\min =\dfrac{13750}{7} $ rad/min
Since in a complete revolution we cover $ 2\pi $ radians, we have
The number of revolutions in 1 min $ =\dfrac{13750}{7\times 2\pi }=\dfrac{625}{2} $
Hence the number of revolutions in 20 mins = $ \dfrac{625}{2}\times 20=6250 $ revolutions, which is the same as obtained above.