Which of the following statements is false for a particle moving in a circle with a constant angular speed?
Correct answer: B. The acceleration vector is tangent to the circle
- A. The velocity vector is tangent to the circle
- B. The acceleration vector is tangent to the circle
- C. The acceleration vector points to the center of the circle
- D. The velocity and acceleration vectors are perpendicular to each other
Explanation
When a particle moves in a circle with constant angular speed, its acceleration is directed towards the centre of the circle. This acceleration, known as centripetal acceleration, is necessary to maintain the circular motion. The velocity, on the other hand, is tangent to the circle and perpendicular to the acceleration. Therefore, the correct statement is that the acceleration vector is tangent to the circle, not the velocity.
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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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