# Uniform solid sphere rolling on inclined plane

• antiparticle
In summary, the formula for the acceleration of a uniform solid sphere rolling on an inclined plane is a = (2/5)g*sinθ, where g is the acceleration due to gravity and θ is the angle of the incline. The mass of the sphere does not affect its acceleration on an inclined plane, as it is determined solely by the angle of the incline and the acceleration due to gravity. Translational motion involves the center of mass moving in a straight line down the incline, while rotational motion involves the sphere rotating around its center of mass. The radius of the sphere does not directly affect its acceleration, but a larger radius may result in a larger moment of inertia. Friction can slow down and eventually stop the
antiparticle

## Homework Statement

A uniform solid sphere,rolls without slipping on a horizontal surface with an angular velocity $$\omega$$,meets a rough inclined plane of incination 60(degrees).The sphere starts pure rolling up the plane with an angular velocity.Find the new angular velocity .

## Homework Equations

Angular momentum conservation about point of contact with the incline.

## The Attempt at a Solution

That means that the sphere has to give up some of its rotational energy to acquire a velocity in a direction it hadn't before.
Find a relationship between momentum and kinetic energy and then resolve.

## 1. What is the formula for the acceleration of a uniform solid sphere rolling on an inclined plane?

The formula for the acceleration of a uniform solid sphere rolling on an inclined plane is a = (2/5)g*sinθ, where g is the acceleration due to gravity and θ is the angle of the incline.

## 2. How does the mass of the sphere affect its acceleration on an inclined plane?

The mass of the sphere does not affect its acceleration on an inclined plane. This is because the acceleration is solely determined by the angle of the incline and the acceleration due to gravity.

## 3. What is the difference between translational and rotational motion in a uniform solid sphere rolling on an inclined plane?

In translational motion, the center of mass of the sphere moves in a straight line down the incline. In rotational motion, the sphere rotates around its center of mass as it moves down the incline.

## 4. What is the relationship between the radius of the sphere and its acceleration on an inclined plane?

The radius of the sphere does not directly affect its acceleration on an inclined plane. However, a larger radius may result in a larger moment of inertia, which could affect the sphere's rotational motion down the incline.

## 5. How does friction affect the motion of a uniform solid sphere on an inclined plane?

Friction can cause the sphere to slow down and eventually come to a stop on the incline. The amount of friction depends on the coefficient of friction between the sphere and the incline's surface. Without friction, the sphere would continue to roll indefinitely on the incline.

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