What is the relationship between the angular velocity (ω) and the linear velocity (v) in circular motion?

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Q: What is the relationship between the angular velocity (ω) and the linear velocity (v) in circular motion?

Solution: The relationship is given by v = ωr, where r is the radius of the circular path.

Steps: 6

Step 1: Understand that angular velocity (ω) measures how fast something is rotating around a circle.
Step 2: Know that linear velocity (v) measures how fast something is moving along the edge of the circle.
Step 3: Identify the radius (r) of the circular path, which is the distance from the center of the circle to the edge.
Step 4: Use the formula v = ωr to find the relationship between linear velocity and angular velocity.
Step 5: Remember that if you increase the radius (r), the linear velocity (v) will also increase for the same angular velocity (ω).
Step 6: Conversely, if you increase the angular velocity (ω), the linear velocity (v) will increase as well, assuming the radius remains constant.