A particle moves in a circular path of radius r with a constant angular speed ω.

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Question: A particle moves in a circular path of radius r with a constant angular speed ω. What is the time period of the motion?

Options:

Correct Answer: T = 2π/ω

Solution:

The time period T = 2π/ω for uniform circular motion.

A particle moves in a circular path of radius r with a constant angular speed ω. What is the time period of the motion?

A particle moves in a circular path of radius r with a constant angular speed ω. What is the time period of the motion?

Correct Answer: T = 2π/ω

Step 1: Understand that the particle is moving in a circle with a constant speed.
Step 2: Know that the angular speed (ω) tells us how fast the particle is moving around the circle.
Step 3: Remember that the time period (T) is the time it takes for the particle to make one complete circle.
Step 4: Use the formula for the time period in uniform circular motion, which is T = 2π/ω.
Step 5: Recognize that 2π represents the full circle (360 degrees) and ω is the angular speed.

Uniform Circular Motion – The motion of an object traveling in a circular path at a constant speed, characterized by a constant angular velocity.
Angular Speed – The rate of change of angular displacement, typically measured in radians per second.
Time Period – The time taken to complete one full cycle of motion, which is inversely related to the angular speed in circular motion.