# What concept describes a force acting on the edge of an object

Consider the following scenario:

When studying forces, we know that when there is an unbalanced force acting on an object (let's say a textbook), the textbook moves in the direction of the unbalanced force. However, in real life, the textbook will move differently if the force is applied on the edge of the textbook versus the center of the textbook.

The force is not applied on an angle; it's applied closer to one edge of the textbook instead of the dead center. The force should move the textbook forward, but instead the book will be pushed forward on the edge only, causing the book to spin.

What concept of forces describes this phenomenon? It can't be a force on an angle because that would still cause the textbook to move in a straight line. I have been trying to research and describe this problem, but I had no success.

The phenomenon you're talking about is torque, which is simply a force acting at a distance from an object's center of mass. If the force vector points directly through the center of mass, you'll just have a translational movement, but if the force vector points anywhere else, you'll induce a rotation that's related to the strength of the force and how far it is from the center of mass.

There's an entire set of equations that govern rotational motion, relating angular acceleration, angular velocity, angular momentum, and rotational energy, which are analogous to the equations of translational motion you may be familiar with.

• Thank you, this helps a lot! – Victor Resnov Oct 1 '19 at 13:06

The force is not applied on an angle; it's applied closer to one edge of the textbook instead of the dead center. The force should move the textbook forward, but instead the book will be pushed forward on the edge only, causing the book to spin.

You need to take into account that there is another force acting on the text book besides the one you apply: Friction.

If there were absolutely no friction on the surface supporting the text book the center of mass will accelerate forward as well as there being rotation about the center of mass. Friction opposes the applied force. This retards the forward motion of the center of mass of the book. So the book spins more than it moves in translation.

I just did this little experiment with my cell phone. It has an Otterbox rubber jacket on it. When I pushed it on the smooth surface of my desk, the edge moved and the phone rotated about the center, but the center stayed pretty much in place. I removed the outer jacket, reducing the friction between the two surface, the phone not only rotated but the center also moved forward.

Hope this helps.

• Thanks for your help! – Victor Resnov Oct 1 '19 at 13:07
• No clue what you mean about the weight of the book being concentrated at the center of mass - the weight is uniformly distributed over the contact surface between the book and the table. There's no more friction at the center than the edge, so that explanation of your experiment makes no sense. – Nuclear Wang Oct 1 '19 at 13:11
• @NuclearWang When you push an object at the edge and it rotates, it rotates around a center point. When doing the phone experiment myself, I found that when the friction changes (due to a different surface), it rotated on a different point. When I took the phone case off, it rotated on a point closer to the center. The opposite happened when the phone case was on. That's what I think he's referring to. – Victor Resnov Oct 1 '19 at 13:34
• @NuclearWang In principle you are right. I will revise. But the main point is the center is retarded from moving due to friction. – Bob D Oct 1 '19 at 13:37
• @VictorResnov Did you also note that the center of the phone moved more in translation with less friction? That is what I observed. – Bob D Oct 1 '19 at 13:38

The other answers are exactly right. When you apply a force to an otherwise free object along a line that is offset from its centre of mass you set-up a torque which causes it to rotate as well as to translate. If friction is present it increases the twisting effect and resists the translational motion.

If you want to develop a clear intuition about why this happens, follow this simple thought experiment...

Imagine you have three bodies, footballs say, floating in a line in free space. To make it easier to describe, suppose they are aligned vertically from your point of view, one at the top, one in the middle and one at the bottom, with say a gap of 20 feet between each one.

Now imagine applying a force to shift the bottom football to the left. It moves but the other two don't- they will stay where they are until a force is applied to them

Now imagine the balls are connected by string. This time, when you start moving the lower ball to the left its string starts moving the middle ball in its direction (downward to the left), and the middle ball in turn starts pulling the top ball after it. The effect is that as you drag the bottom ball to the left, the other two balls are pulled into line behind it, so the whole arrangement is rotated by 90 degrees as well as moving to the left. The top and middle ball are not being directly moved by the force you have applied to the bottom ball- its is the force between the balls which is causing them to move, and since that's in a different direction to your force it causes a turning effect.