Question

A particle moves along a circular path of radius \( r \) with uniform speed \( V \). The angle described by the particle in one second is

• A. \( V r \)
• B. \( \frac{r}{V} \)
• C. \( V^2 r \)
• D. \( \frac{V}{r} \)

Hint:

In uniform circular motion, the angular velocity is given by \( \frac{V}{r} \), where \( V \) is the speed and \( r \) is the radius of the circle.

Answer 1

The Correct Option is D

Step 1: Understanding the concept of angular velocity.
In uniform circular motion, the angle \( \theta \) described by the particle per unit time is related to the angular velocity, which can be expressed as: \[ \theta = \frac{V}{r} \] where \( V \) is the linear velocity of the particle and \( r \) is the radius of the circular path. This equation represents the angular velocity in radians per second. Step 2: Derivation of the angle.
The angular velocity, \( \omega \), is given by the formula: \[ \omega = \frac{V}{r} \] Since the angle described by the particle in one second is the angular velocity, we conclude that in one second, the angle \( \theta \) is equal to \( \frac{V}{r} \) radians. Step 3: Final Answer.
Thus, the correct answer is \( \frac{V}{r} \), which corresponds to option (D).