What Is the Acceleration of a Rolling Sphere on an Inclined Plane?

AI Thread Summary
The acceleration of a solid sphere rolling down a 30-degree inclined plane is influenced by multiple forces, including gravity, friction, and the normal force. While the gravitational component along the incline is mg sin(θ), it is not the sole factor determining acceleration. To find the acceleration, both translational and rotational dynamics must be considered, applying Newton's second law. The concept of "rolling without slipping" indicates that the sphere completes one full revolution for every distance of 2πR traveled. Understanding these principles is crucial for accurately calculating the sphere's center of mass acceleration.
UrbanXrisis
Messages
1,192
Reaction score
1
A solid shere of mass M and radius R rolls without slipping down an inclined plane whose incline angle with the horizontal is 30 degrees. What is the acceleration of the sphere's center of mass?

gsinX is the acceleration, so it would be g/2 right?
 
Physics news on Phys.org
No. While mg \sin \theta is the component of the ball's weight along the incline, it is not the only force acting on the ball.
 
A solid shere of mass M and radius R rolls without slipping down an inclined plane whose incline angle with the horizontal is 30 degrees.
 
still not sure what you mean... so it doesn't slip, so what?
 
Start by identifying all the forces acting on the sphere. (Hint: I count 3)
 
force of friction, normal force, and force of gravity
 
Right. To solve for the acceleration, you'll need to apply Newton's 2nd law for both translation and rotation.
 
The point of "rolling without slipping" is that the sphere makes on complete revolution while going a distance 2\pi R
 

Similar threads

Why is the direction of kinetic/static friction up a ramp?
Replies
7
Views
1K
Acceleration of system related to rolling motion and pulley
Replies
35
Views
4K
Rolling without slipping down an inclined plane
Replies
18
Views
5K
Possible to use work-energy theorem from a non-inertial frame?
Replies
1
Views
2K
Rolling without slipping problem
Replies
42
Views
3K
Wooden sphere rolling on a double metal track
2
Replies
97
Views
5K
Required force for sphere start rolling
Replies
2
Views
669
Mass slipping on a moving inclined plane
Replies
5
Views
1K
Conservation of energy problem: Ball rolling down inclined plane and then through a loop-the-loop
Replies
10
Views
2K
Rolling Down an Off Center Cylinder on an Incline
Replies
2
Views
1K

Hot Threads

Recent Insights

Back
Top