Question

14. A drive shaft of radius 15 cm has an angular frequency of 100 rpm. Determine

a) The tangential velocity

b) The centripetal acceleration

Answer 1

Let $R = 15cm = 0.15m$ be the radius, and $f = 100rpm = 5/3Hz$ be the angular frequency. By defintion, the period of motion (time of one revolution) is:

$$T = \dfrac{1}{f}$$

The tangential velocity is then the full circule length divided by period:

$$v = \dfrac{2\pi R}{T} = 2\pi R f\\ v = 2\pi \cdot 0.15\cdot \dfrac53 \approx 1.57 m/s$$

The centripetal acceleration is:

$$a = \dfrac{v^2}{R}\\ a = \dfrac{1.57^2}{0.15} \approx 16.4m/s^2$$

Answer. a) 1.57 m/s, b) 16.4 m/s^2.