An object travels at constant speed arround a circle of radius 1.0m in 1.0s. What is the magnitude of its acceleration?
Correct answer: D. 4π2 ms-2
- A. Zero
- B. 1.0 ms-2
- C. 2π2 ms-2
- D. 4π2 ms-2
Explanation
In this problem, the object is moving in a circular path with a constant speed. While the speed remains constant, the direction of the object's velocity is continuously changing, which results in centripetal acceleration. The formula for centripetal acceleration, a = v2/r, is essential here. The speed of the object can be calculated as the distance traveled in one revolution (which is 2π meters) divided by the time taken (1 second), giving a speed of 2π m/s. Plugging this value into the formula gives:a = (2π)2/1 = 4π2 ms-2. Thus, Option D is the correct answer. Options A and B are incorrect as they overlook the acceleration due to the change in direction in circular motion, while Option C miscalculates the centripetal acceleration based on the given parameters.
This question appeared on the ETEA MDCAT 2014 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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