Question

A car revolves in the circle by the specs of 10m/s. It the radius of the circle is 0.2m then

Find the angular velocity

Find the angular acceleration

Find the tangential velocity

Find the radial force and centereiptal

Answer 1

(a)

$$\omega=\dfrac{v}{r}=\dfrac{10\ \dfrac{m}{s}}{0.2\ m}=50\ \dfrac{rad}{s}.$$

(b) Unfortunately we don't know the time that the car takes to reach final angular velocity. Let's suppose that $t=5\ s$. Then, we can find angular acceleration as follows:

$$\alpha=\dfrac{\omega-\omega_0}{t}=\dfrac{50\ \dfrac{rad}{s}-0}{5\ s}=10\ \dfrac{rad}{s^2}.$$

(c) Tangential velocity is given:

$$v=10\ \dfrac{m}{s}.$$

(d) The centripetal (or radial) force can be found as follows:

$$F_c=ma_c=m\dfrac{v^2}{r}.$$

Unfortunately, we don't know the mass of the car. Let's assume that the mass of the car is 50 kg.

Then, we get:

$$F_c=50\ kg\cdot\dfrac{(10\ \dfrac{m}{s})^2}{0.2\ m}=25000\ N.$$