Question

an object is undergoing a uniform circular motion. what can one say about its acceleration? multiple choice impossible to determine since the speed of the rotating object is not given. the acceleration has a constant direction, but its magnitude changes continuously. the acceleration has a constant magnitude, but its direction changes continuously. the acceleration is constant in both magnitude and direction.

Explanation:

In uniform circular motion, the speed (magnitude of velocity) is constant, but velocity direction changes (tangential to the circle). Acceleration in this motion is centripetal, directed toward the center. As the object moves, the center - pointing direction of acceleration changes continuously, but its magnitude ($a = \frac{v^{2}}{r}$ or $a=\omega^{2}r$, where $v$ is speed, $r$ is radius, $\omega$ is angular velocity) remains constant as long as $v$ (or $\omega$) and $r$ are constant.

• The first option is wrong because we know the nature of acceleration in uniform circular motion without the specific speed value.
• The second option is wrong as the magnitude of acceleration is constant.
• The fourth option is wrong because the direction of acceleration (toward the center) changes as the object moves along the circular path.

Answer:

The acceleration has a constant magnitude, but its direction changes continuously.