A body rotates with uniform speed in a circle of radius r and takes time T to complete one revolution. What are the magnitude of the angular velocity ω, the linear velocity v and the acceleration a ?
Correct answer: B. w=2π/T, v=2πr/T, a=4π2r/T2
- A. w=1/T, v=4πr/T, a=2πr/T2
- B. w=2π/T, v=2πr/T, a=4π2r/T2
- C. w=2π/T, v=2πr/T, a=2πr/T2
- D. w=2π/T, v=4πr/T, a=4π2r/T2
Explanation
The correct option is b), where the magnitudes of the angular velocity, linear velocity, and acceleration are w=2π/T, v=2πr/T, a=4π2r/T2, respectively.The angular velocity is defined as the angle rotated per unit time. For one complete revolution, the angle rotated is 2π radians, and the time taken is T. (w=2π/T)The linear velocity is defined as the distance travelled per unit time. For one complete revolution, the distance travelled is the circumference of the circle, 2πr, and the time taken is T. (v=2πr/T)The acceleration for uniform circular motion is centripetal acceleration, directed towards the centre, with magnitude given by a=4π2r/T2.
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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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