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Excerpt
hiddentrue

Find the acceleration of a ball rolling without slipping on an inclined plane.

Composition Setup

Consider a ball placed on a ramp inclined at θ = 30° above the horizontal.

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Card
labelPart A

Part A

What is the acceleration of the ball's center of mass as it rolls down the ramp? Assume that the ball rolls without slipping.

Solution

We consider two methods.

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Card
labelMethod 1: Dynamics

Method 1: Dynamics

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System:
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The ball is treated as a .

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External influences from the earth (gravity) and the ramp (friction and normal force).

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Model:
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plus

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Approach:

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External influences from the earth (gravity) and the ramp (normal force and friction).

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Model:
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.

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Approach:

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Approach:

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Method 1
Method 1

Card
labelMethod 2: Energy

Method 2: Energy

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System:
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The ball plus the earth and ramp.

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There are internal gravity, normal and friction forces. Gravity is conservative, while the normal force and friction are non-conservative.

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Model:
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.

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Approach:

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Method 2
Method 2

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Part B
Part B

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