A body moves in a circle with increasing angular velocity. At time t= 6sec, the angular velocity is 27rad/s. What is the radius of circle made by the body where linear velocity is 81cm/s?
Correct answer: C. 3cm
- A. 6cm
- B. 9cm
- C. 3cm
- D. 7cm
Explanation
Given the linear velocity of 81 cm/s and the angular velocity of 27 rad/s, we can use the formula v = r * ω to find the radius. By converting the linear velocity to meters per second, we get 0.81 m/s. Solving for the radius, we find that it is approximately 0.03 meters or 3 centimetres. This makes Option C the correct answer. The other options are incorrect due to errors in the calculations or misinterpretation of the given data.v = rω ⇒ r = v/ω = 81/27 = 3cm
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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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