Question

An object is being rotated in a centrifuge which has a radius of 6.0 m. If the
acceleration of the centrifuge is 3 g, calculate the velocity of object and the time
period of its motion.

Answer 1

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Answer 2

The velocity of the object is the linear velocity.

The relationship between angular acceleration and linear velocity is as follows.

Ac = v²/r

Ac = is the angular acceleration.

V = the linear velocity.

r = the radius of the centrifuge.

Doing the substitution we have :

3 = v²/6

3 × 6 = v²

v² = 18

v = √18

v = 4.24 m/s

The relationship between the angular velocity and angular acceleration is :

Ac = rω

3 = 6ω

ω = 3/6

ω = 0.5

The period T is given by :

T = 2π/ω

T = (2 × 22/7)/0.5

= 12.57 Seconds