Gravity and torque on balls rolling down an incline

[lsginn]

What is the significance of gravity on the torque of balls rolling down an incline?

I know that gravity is able to exert a force, or torque by acting on the center of mass, causing an object to rotate. But what about rolling motion? Where would the axis of rotation be for a ball rolling down an incline?

Also, in terms of gravity, what does it mean for a ball to have a large/small moment of inertia and torque. Does this show anything about the effects of gravity on balls that have large/small moments of inertia and torque?

Relevant equations:
T=Ia
Tgrav=-mgx(cm)

 

[Simon Bridge]

This is homework?

What is the significance of gravity on the torque of balls rolling down an incline?

It provides the torque.

I know that gravity is able to exert a force, or torque by acting on the center of mass, causing an object to rotate. But what about rolling motion? Where would the axis of rotation be for a ball rolling down an incline?

Draw the situation and draw in the gravity force. Draw in the friction force. If it were not a ball, but a tall narrow pin or something, you'd have no trouble with the idea that it would fall over down the slope would you. Where is the pivot point in that situation? Can you relate this to the ball?

For the others, you need to relate the torque due to gravity with the acceleration of the ball.
Moment of inertia is a standard concept in rotational motion - so it means what it always means.
See also: http://www.real-world-physics-problems.com/rolling-without-slipping.html

 

[rcgldr]

Gravity effectively acts on the center of mass of the ball, so it's not generating any torque. Friction force from the incline acts at the surface of the ball, opposing gravity somewhat, and generates the torque. If the incline had zero friction, there would be no torque, and the ball would slide and not rotate.