An object travels at constant speed around a circle of radius 1.0 m in 1.0 s. what is the magnitude of its acceleration?
Correct answer: D. 4π2 ms-2
- A. Zero
- B. 1.0 ms-2
- C. 2π ms-2
- D. 4π2 ms-2
Explanation
To find the magnitude of the acceleration of an object moving in a circle, we use the formula for centripetal acceleration: a = ω²r. In this case, the angular velocity ω is 2π rad/s because the object completes one full circle (2π radians) in 1 second. The radius r is given as 1.0 m. Substituting these values, we find that the acceleration a = (2π)²(1) = 4π² ms-2.The other options are incorrect because they either assume no acceleration (which ignores the change in direction), or they use incorrect calculations or interpretations of the formula for centripetal acceleration.
This question appeared on the ETEA MDCAT 2013 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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