A sphere rolls without slipping on a flat surface. If it has a radius R and roll

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

Options:

Correct Answer: v/R

Solution:

The angular speed ω of a rolling sphere is given by ω = v/R.

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

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

Step 1: Understand that a sphere rolling without slipping means that the point of contact with the surface is not sliding.
Step 2: Recall the relationship between linear speed (v) and angular speed (ω) for rolling objects.
Step 3: The formula that relates linear speed to angular speed is ω = v/R, where R is the radius of the sphere.
Step 4: Identify the values: you have the speed (v) and the radius (R) of the sphere.
Step 5: Use the formula ω = v/R to calculate the angular speed.

Rolling Motion – The relationship between linear speed and angular speed for objects rolling without slipping.
Angular Speed – The rate of rotation of an object, defined as the angle rotated per unit time.
Radius and Velocity Relationship – The formula ω = v/R shows how the radius of the sphere affects its angular speed.