When a wheel rolls without slipping, what is the acceleration of its center of mass if it rolls down an incline with angle θ?

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Q: When a wheel rolls without slipping, what is the acceleration of its center of mass if it rolls down an incline with angle θ?

Solution: The acceleration of the center of mass of a wheel rolling down an incline is g sin(θ).

Steps: 5

Step 1: Understand that when a wheel rolls down an incline, it experiences gravitational force acting on it.
Step 2: Recognize that the incline has an angle θ, which affects how gravity pulls the wheel down the slope.
Step 3: Identify that the component of gravitational force acting along the incline is given by g sin(θ), where g is the acceleration due to gravity.
Step 4: Realize that for a wheel rolling without slipping, the acceleration of its center of mass is equal to this gravitational component.
Step 5: Conclude that the acceleration of the center of mass of the wheel rolling down the incline is g sin(θ).