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Rolling down an incline
Intermediate
Rolling bodies accelerate slower than sliding ones due to rotational energy.
a = g sinθ/(1+I/mR²)a = g sinθ/(1 + I/mR²). Smaller I/mR² means faster descent.
Solid sphere (2/5): a = 0.71 g sinθ. Ring: 0.5 g sinθ.
Mass and radius cancel out.
In more detail
A body rolling down an incline without slipping converts potential energy into translational and rotational kinetic energy. The acceleration depends on how the mass is distributed.
Real-world uses
- Physics labs measure the moment of inertia of rolling objects using ramps.
- Designing racing bikes and wheels involves considering rolling acceleration.
- Balls rolling down a ramp in a classroom experiment accelerate more slowly than a sliding block, because part of the energy spins the ball.
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Frequently asked questions
Which body reaches the bottom first?
The one with the smallest moment of inertia relative to its mass, such as a solid sphere.
Does the radius matter?
Not for a given shape, since the acceleration is independent of radius for the same shape.
Does the mass of the rolling ball change the acceleration?
No. The mass cancels, so the acceleration depends only on the slope angle and the shape of the object through I/mR².
Related topics in Rotational Motion
Newton's second law for rotation · Rotational kinetic energy · Rolling without slipping · Race of rolling bodies · Work and power in rotation · Angular momentum of a particle