Classical Mechanics

37.2 Worked Example - Wheel Rolling Without Slipping Down Inclined Plane

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A cylinder of radius ${\displaystyle R}$, mass ${\displaystyle M}$, and moment of inertia ${\displaystyle I_{cm}}$ about the axis passing through its center of mass starts from rest and moves down an inclined at an angle ${\displaystyle \varphi }$ from the horizontal. The center of mass of the cylinder has dropped a vertical distance ${\displaystyle h}$ when it reaches the bottom of the incline. The cylinder rolls down the incline without slipping. Use the conservation of energy principle to calculate the speed of the center of mass of the cylinder when it reaches the bottom of the incline. Express your answer in terms of ${\displaystyle m}$, ${\displaystyle h}$, ${\displaystyle R}$, ${\displaystyle g}$, and ${\displaystyle I_{cm}}$.

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