# Rolling Motion of a Sphere

1. Nov 21, 2008

### zmike

A perfect uniform sphere is thrown horizontally on to the floor. It slides on the floor then it begins rollings soon after. Draw a complete FBD and diagram for the motion before and after the rolling.

->My problem is does the kinetic friction act in the same direction as the balls motion or opposite to it BEFORE it begins to roll?

->Do I draw kinetic friction acting on the center of the mass of the ball BEFORE it rolls? or does it only act on the bottom edge of the ball?

it seems to me that friction can only act on the bottom but in previous units in the textbook, friction appears to act on the center of mass???

2. Nov 21, 2008

### Staff: Mentor

Friction acts at the point of contact, where ball and floor meet. As far as the direction in which friction acts, what do you think?

3. Nov 21, 2008

### zmike

I think that if the sphere is slipping and not rolling then it acts on the center of mass therefore the friction produces NO torque. Is that correct? b/c my textbooks doesn't accurately describe the motion.

4. Nov 22, 2008

### Staff: Mentor

No, that's not correct. For one thing, friction is a contact force, not a long range force, so it always acts at the point of contact. As soon as the ball hits the floor, friction acts to make it start rolling (by exerting a torque) and to slow it down (due to it's effect on the linear motion of the center of mass).

Realize that you can use the net force on an object to determine the acceleration of its center of mass regardless of where the actual forces act on the object.

What does your textbook say exactly?

5. Nov 22, 2008

### zmike

How is it possible for an object to be slipping while there is a torque acting on it? b/c there is no equation that can describe that sort of motion in my textbook)

->My textbook states that an object can only either be
1) Rolling and not slipping (torque/friction acting on point of contact)
2) Slipping and not rolling

It sounds like that if there is torque, there cannot be slipping

I would expect for the 2nd case that friction acts against the direction of motion on the CENTER OF MASS (just like with FBD of linear motion of a box being pushed, in the FBD you would draw friction extending from the center of mass). If the friction only acts on the bottom of the sphere then my FBD wouldn't make any sense, since there would be no friction slowing down the point at the center of mass.

Thanks

Last edited: Nov 22, 2008
6. Nov 22, 2008

### Staff: Mentor

"Slipping" just means that the point of contact is sliding along the surface. If there's a torque on it, it will both slide and roll.
What book are you using?

That's not true. Let's stick to the case of a horizontal surface. The object can:
1) Roll without slipping. Note that once this condition is realized the friction force becomes zero.
2) Slip without rolling. (Otherwise known as pure "sliding".) This happens if there's no friction.
3) Roll with slipping. When you first drop that ball onto the surface with a forward velocity, the ball will both slip and begin to roll (due to the torque from friction).

Nah.

This is incorrect thinking for several reasons:

(1) Friction always acts at the point of contact. It would be quite magical if it could act somewhere else.

(2) For the purpose of analyzing the translational motion, it doesn't matter where the force acts. Its effect on the center of mass will be the same. The friction force at the point of contact will most definitely act to slow down the sliding ball.

(3) The force of friction does two things: It produces an acceleration of the center of mass (negative, in this case, slowing the ball down) and it produces a torque about the center of mass, which starts the ball rolling faster and faster. At some point, when the translational and angular speed meet the condition for "rolling without slipping" (v = ωr), then it will maintain that speed (under perfect conditions, of course).

7. Nov 22, 2008

### zmike

thanks,

one last thing, if there is a non-zero torque on an object, wouldn't that mean the object must be rolling?

so in this case, why is the sphere sliding (translational motion) while there is a torque caused by friction? yet once it's speed drops it beings to roll? Since the force of friction doesn't change, why would it not roll initially (and only slide)?

thanks

Last edited: Nov 22, 2008
8. Nov 23, 2008

### Staff: Mentor

A non-zero torque means that the object has an angular acceleration, thus its rotational speed is changing.

Why not? You seem to be stuck with the idea that something is either rolling but not sliding or sliding but not rolling. The sphere has no problem both sliding and rolling.

The sphere continues to slide because its translational speed (v) is greater than the rotational speed about the center (ωr).
It begins rolling immediately, but it's still sliding as well. (It starts with zero rotational speed.)

Consider this similar problem. What if you gently dropped onto the floor a rotating ball which had no translational speed? What happens then? What does the friction force do?

9. Nov 23, 2008

### zmike

Thanks,

but would it be possible for an object to exhibit no rolling and only sliding while there is torque acting on the object in 1 direction?

-> Regarding the direction of the friction. If the sphere ended with a positive angular velocity (it rotates clockwise). Doesn't that mean that friction must be in the same direction of motion as the sphere? or else why would it's angular velocity be increasing in that direction?

Common sense tells me that it would move forward if w is positive but that would mean that friction force is in the same direction of the motion of the ball which seems odd. How does friction which is suppose to slow things down, speed the ball up?

Last edited: Nov 23, 2008
10. Nov 23, 2008

### Staff: Mentor

No.

The direction of angular velocity increase is given by the direction of the torque. Since friction, which points in a direction opposite to the translational motion of the sphere, creates a clockwise torque the angular velocity increases in the clockwise direction. Of course, since friction opposes the direction of the translational motion, the ball's translational speed decreases.

Friction always acts to oppose slipping between surfaces. In this case, the ball's surface is slipping clockwise (towards the left), thus friction will act towards the right. This time the ball's rotational speed decreases while its translational speed increases.