A ball rolls without slipping on a flat surface. If its radius is R and it has a linear speed v, what is its angular speed?

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Q: A ball rolls without slipping on a flat surface. If its radius is R and it has a linear speed v, what is its angular speed?

Solution: The relationship between linear speed and angular speed for rolling without slipping is ω = v/R.

Steps: 6

Step 1: Understand that the ball is rolling without slipping. This means that the point of contact between the ball and the surface is not sliding.
Step 2: Know that linear speed (v) is how fast the ball is moving in a straight line.
Step 3: Understand that angular speed (ω) is how fast the ball is spinning around its center.
Step 4: Remember the formula that relates linear speed and angular speed for rolling without slipping: ω = v/R.
Step 5: Identify R as the radius of the ball. This is the distance from the center of the ball to the edge.
Step 6: To find the angular speed (ω), divide the linear speed (v) by the radius (R).