If a wheel of radius R rolls without slipping, what is the distance traveled by

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Question: If a wheel of radius R rolls without slipping, what is the distance traveled by the center of mass after one complete rotation?

Options:

Correct Answer: 2πR

Solution:

The distance traveled by the center of mass after one complete rotation is equal to the circumference of the wheel, which is 2πR.

If a wheel of radius R rolls without slipping, what is the distance traveled by the center of mass after one complete rotation?

If a wheel of radius R rolls without slipping, what is the distance traveled by the center of mass after one complete rotation?

Step 1: Understand that the wheel rolls without slipping, meaning the distance it rolls is directly related to its rotation.
Step 2: Recall the formula for the circumference of a circle, which is 2πR, where R is the radius of the wheel.
Step 3: Recognize that when the wheel makes one complete rotation, the distance traveled by the center of mass is equal to the circumference of the wheel.
Step 4: Conclude that the distance traveled by the center of mass after one complete rotation is 2πR.

Rolling Motion – Understanding how a wheel rolls without slipping and the relationship between the distance traveled and the wheel's circumference.
Circumference Calculation – Calculating the circumference of a circle using the formula 2πR.