A body moves in a circle with increasing angular velocity. At time t =6 sec, the angular velocity is 27 rad/s. What is the radius of the circle made by the body where linear velocity is 81 cm/s?
Correct answer: C. 3 cm
- A. 6 cm
- B. 9 cm
- C. 3 cm
- D. 7 cm
Explanation
The following is the solution:v = ω x r Given that the linear velocity is 81 cm/s and the angular velocity is 27 rad/s, we can substitute these values into the formula: 81 cm/s = 27 rad/s x r Simplifying the equation: r = 81 cm/s / 27 rad/s r = 3 cm.
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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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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?