A circular disc of mass M and radius R is rotating about it's with uniform speed v. Its kinetics energy is:
Correct answer: C. ¼ Mv2
- A. Mv2
- B. ½ Mv2
- C. ¼ Mv2
- D. 1/8 Mv2
Explanation
The kinetic energy of the rotating disc can be calculated as:KE = (1/2) I ω^2where I is the moment of inertia and ω is the angular velocity.For a uniform circular disc rotating about its centre,I = (1/2) M R^2andω = v/RSubstituting these values in the formula for kinetic energy, we get:KE = (1/2) (1/2) M R^2 (v/R)^2Simplifying, we get:KE = (1/4) M v^2Therefore, the kinetic energy of the rotating disc is (1/4) M v^2.As it is numerical, it can have only one possible answer.
This question appeared on the ETEA MDCAT 2017 paper, which you can sit online with every answer explained.
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About Angular and Linear Quantities
Rotational motion relates angular displacement, angular velocity and angular acceleration to linear displacement, tangential velocity and tangential acceleration through the radius. Questions use radians, v equals r omega and tangential acceleration, while distinguishing tangential velocity from centripetal acceleration and angular quantities from their linear counterparts.
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