# A rolling ball accelerating down an incline

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1. Oct 16, 2015

### Mr Sun

1. The problem statement, all variables and given/known data

source:http://www.wired.com/2014/07/a-rolling-object-accelerating-down-an-incline/

For a ball rolling on an incline, I know how to calculate the acceleration. However, I am quite confused about a situation. What if static friction acting on the ball is equal to the component of gravity along the plane, which means, net force acting on the ball is zero. But net torque of the ball is not zero, which means the ball is supposed to rotate. Under this situation, either the ball rolling down or not is quite confusing. Considering net force, it should not have translation. but considering net torque, it should rotate, and then roll down.

What will happen ? Is there any mistake on my analysis ? Please help! Thanks a lot!

2. Oct 16, 2015

### J Hann

There are 2 ways to solve this problem.
(1) You can take torque about the point of contact with the plane (using the parallel axis theorem).
In this case the frictional force does not enter into the solution.
(2) You can take torque about the center of mass with the frictional force providing the torque.
Here you also have to consider the net translational force on the object and then
you can eliminate the frictional force from the resulting equations.

3. Oct 16, 2015

### Mr Sun

But is there any problem in my understanding? Why will a ball translate while net force is zero?

4. Oct 16, 2015

### ehild

Static friction is not a force of definite value. It gets a value what is necessary for rolling. That force can not be greater than μsFN. If the component of gravity is greater than this maximum force of static friction, the friction becomes kinetic and the ball will slip. But the force of static friction can be anything smaller then the maximum value.

5. Oct 16, 2015

### J Hann

If the frictional force equaled the component of the gravitational force along the plane the net translational force would be zero.
This contradicts the fact that frictional force supplies the torque that causes the ball to roll.
You can verify this by calculating the actual forces (frictional and translational) and show that they are not equal.
If they are equal then Newton's laws are invalid.
Obviously, the system is in unstable equilibrium, and the ball is going to move.
Try balancing a pencil on its point and say that the pencil will not fall because the frictional
force on the point of the pencil balances the gravitational force that acts on the center of mass of
the pencil so the center of mass of the pencil will not move.

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