# I Will a sphere rotate on a frictionless inclined surface?

Tags:
1. Dec 27, 2017

### jbriggs444

There is no torque about its center of mass (on which point I agree with @CWatters). So it will not spin.

More generally, it will slide if its linear acceleration exceeds its rotational acceleration multiplied by its radius. Since its rotational acceleration is zero and its linear acceleration is non-zero, this condition is trivially met. You would typically determine the two accelerations by drawing free body diagrams, determining relevant forces and solving the resulting equations.

2. Dec 27, 2017

### PeroK

The key piece of information is the maximum friction force.

As I mentioned in an earlier post, you should study a sphere and/or a cylinder moving down a frictional slope.

3. Dec 27, 2017

### CWatters

A free body diagram of the ball has no "point of contact", just the ball and the forces acting on it. No?

4. Dec 27, 2017

### jbriggs444

A free body diagram used for computing torque most certainly has the points where forces act and where the axis of rotation is assigned.