the circular motion of a particle with constant speed is

Options

A. Simple harmonic but not periodic
B. Periodic and simple harmonic
C. neither periodic nor simple harmonic
D. periodic but not simple harmonic

Answer

To analyze the circular motion of a particle with constant speed, we can break down the problem into several steps:

### Step-by-Step Solution:

1. **Understanding Circular Motion**:
- A particle moving in a circular path is undergoing circular motion. In this case, the motion is described as uniform circular motion because the speed of the particle remains constant.

2. **Defining Key Terms**:
- **Speed**: The magnitude of the velocity of the particle, which remains constant in this scenario.
- **Velocity**: A vector quantity that has both magnitude and direction. Although the speed is constant, the direction of the velocity vector changes continuously as the particle moves along the circular path.

3. **Centripetal Acceleration**:
- Even though the speed is constant, the particle experiences centripetal acceleration directed towards the center of the circular path. This acceleration is responsible for changing the direction of the velocity vector.
- The formula for centripetal acceleration (\(a_c\)) is given by:
\[ a_c = \frac{v^2}{r} \]
where \(v\) is the constant speed and \(r\) is the radius of the circular path.

4. **Centripetal Force**:
- To maintain circular motion, a net inward force (centripetal force) is required. This force can be provided by tension, gravity, friction, or any other force depending on the context.
- The net centripetal force (\(F_c\)) is given by:
\[ F_c = m \cdot a_c = m \cdot \frac{v^2}{r} \]
where \(m\) is the mass of the particle.

5. **Conclusion**:
- The motion of the particle is classified as uniform circular motion because it travels along a circular path at a constant speed, but with a continuously changing velocity due to the change in direction.