Question

A particle is being rotated in a centrifuge which has a radius of 5.0 m. If the 

particle’s centripetal acceleration is 4 g, determine its speed. What is the time period 

of its motion?

Answer 1

a) By the definition of the centripetal acceleration, we have:

$$a_c=\dfrac{v^2}{r},$$ $$v=\sqrt{a_cr}=\sqrt{4\cdot9.8\ \dfrac{m}{s^2}\cdot5.0\ m}=14\ \dfrac{m}{s}.$$

b) Let's first find the angular velocity from the formula:

$$v=\omega r,$$ $$\omega=\dfrac{v}{r}=\dfrac{14\ \dfrac{m}{s}}{5.0\ m}=2.8\ \dfrac{rad}{s}.$$

Finally, we can find the time period of particle's motion from the formula:

$$T=\dfrac{2\pi}{\omega}=\dfrac{2\pi}{2.8\ \dfrac{rad}{s}}=2.24\ s.$$

Answer:

a) $v=14\ \dfrac{m}{s}.$

b) $T=2.24\ s.$