A body moving in a circular path of radius \( r \) has tangential acceleration and centripetal acceleration. If the body is moving at constant speed \( v \), what are the magnitudes of tangential and centripetal accelerations
Correct answer: B. Tangential acceleration \(= v^2/r\) and Centripetal acceleration \(= 0\)
- A. Tangential acceleration \(= rv^2\) and Centripetal acceleration \(= 0\)
- B. Tangential acceleration \(= v^2/r\) and Centripetal acceleration \(= 0\)
- C. Tangential acceleration \(= 0\) and Centripetal acceleration \(= rv^2\)
- D. Tangential acceleration \(= 0\) and Centripetal acceleration \(= v^2/r\)
Explanation
When a body moves at a constant speed in a circular path, its tangential acceleration is \(a_t = \frac{v^2}{r}\) and its centripetal acceleration is \(a_c = 0\).
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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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