Answer to Question #168654 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 first find the angular velocity of the bike:

$$\omega_0=\dfrac{v}{r}=\dfrac{5\ \dfrac{m}{s}}{0.25\ m}=20\ \dfrac{rad}{s}.$$

We can find the number of revolutions from the kinematic equation:

$$\theta=\omega_0t+\dfrac{1}{2}\alpha t^2.$$

Since, the bike moves with constant speed, we get:

$$\theta=\omega_0t=20\ \dfrac{rad}{s}\cdot15\ s\cdot\dfrac{1\ rev}{2\pi\ rad}=47.8\ rev.$$