Answer to Question #168647 in Physics for Hana

Question

The bike is moving at a speed of 18 km / h. The wheel of the bicycle has a radius of 25 cm. How many revolutions does it make in 15s.

Answer 1

Let's change the frame of reference, and consider the situation from the wheel's center perspective. In this frame of reference all points of the wheel move with speed $v = 18km/h = 5m/s$ in the circle. Thus, in $t = 15s$ a point on the wheel cover the following distance:

$$d = vt = 75m$$

This distance correspondes to the following amount of revolution:

$$N = \dfrac{d}{2\pi R}$$

where $2\pi R$ is the length of the wheel ($R = 25cm = 0.25m$). Finally, obtain:

$$N = \dfrac{75}{2\pi\cdot 0.25} \approx 47.7$$

Answer. 47.7.