Question #156139

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?


1
Expert's answer
2021-01-19T07:11:48-0500

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


ac=v2r,a_c=\dfrac{v^2}{r},v=acr=49.8 ms25.0 m=14 ms.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=ωr,v=\omega r,ω=vr=14 ms5.0 m=2.8 rads.\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=2πω=2π2.8 rads=2.24 s.T=\dfrac{2\pi}{\omega}=\dfrac{2\pi}{2.8\ \dfrac{rad}{s}}=2.24\ s.

Answer:

a) v=14 ms.v=14\ \dfrac{m}{s}.

b) T=2.24 s.T=2.24\ s.


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