A body moves in a circle with increasing angular velocity, at time 't'=6s the angular velocity is 27 rad/s... What is the radius of circle where linear velocity is 81cm/s:
Correct answer: D. 3cm
- A. 6cm
- B. 9cm
- C. 7cm
- D. 3cm
Explanation
So here we use the relation between linear and angular quantity i.e. Vt=𝝎r Rearranging the expression, we get r=Vt/𝝎 Here Vt is linear velocity r is radius of the circle And 𝜔 is angular velocity = 81/27 = 3cm Therefore the radius of the circle is 3cm. Note: we do not need to convert the unit of linear velocity i.e cm/s into m/s as all the answers are already given in cm.
This question appeared on the UHS MDCAT 2017 paper, which you can sit online with every answer explained.
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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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