When a wheel rolls without slipping, what is the relationship between the distan

When a wheel rolls without slipping, what is the relationship between the distance traveled by the center of mass and the angle rotated?

When a wheel rolls without slipping, what is the relationship between the distance traveled by the center of mass and the angle rotated?

Step 1: Understand that when a wheel rolls without slipping, it moves forward while also rotating.
Step 2: Identify the radius (R) of the wheel, which is the distance from the center of the wheel to its edge.
Step 3: Recognize that the angle (θ) represents how much the wheel has rotated, measured in radians.
Step 4: Realize that for every complete rotation of the wheel, the distance it travels forward is equal to the circumference of the wheel, which is 2πR.
Step 5: Note that if the wheel rotates by an angle θ (in radians), the distance traveled by the center of mass (d) is directly proportional to both the radius and the angle rotated.
Step 6: Write the relationship as a formula: d = Rθ, where d is the distance traveled, R is the radius, and θ is the angle in radians.

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