Question

The circular motion of a particle with constant speed is:

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

Answer 1

The Correct Option is D

To determine whether the circular motion of a particle with constant speed is simple harmonic or periodic, let's understand the definitions of these concepts:

• Periodic Motion: A motion that repeats itself at regular intervals of time. In the case of circular motion, as the particle moves around the circle, it repeats its position after completing one full revolution; therefore, it is periodic.
• Simple Harmonic Motion (SHM): A type of periodic motion where the restoring force is directly proportional to the displacement and acts in the direction opposite to that of displacement. SHM is characterized by oscillatory motion back and forth through an equilibrium position, like that of a pendulum or a mass on a spring.

Now, let’s analyze the problem:

• In circular motion with constant speed, the particle moves around the circle at a uniform rate. The motion is periodic because it repeats after every complete circle.
• However, the motion is not simple harmonic because the particle does not oscillate back and forth through an equilibrium position. Instead, it maintains a constant distance from the center of the circle, and there is no restoring force proportional to displacement.

Let's rule out the incorrect options:

• Simple harmonic but not periodic: This option is incorrect because circular motion is periodic, not simple harmonic.
• Periodic and simple harmonic: This option is incorrect because, although the motion is periodic, it is not simple harmonic.
• Neither periodic nor simple harmonic: This option is incorrect because the motion is definitely periodic.

Therefore, the correct answer is that the circular motion of a particle with constant speed is periodic but not simple harmonic.