PHYS140 FAQ

Q. In lecture and in DR, we saw two balls crash into two wooden blocks. One ball was like a superball and the other was made out of clay. The block that the superball hit fell over, while the block that the clay ball hit did not. I don't get it -- what happened?

A. Check out this movie that I made:

Blocks and balls movie, quicktime format

Blocks and balls movie, avi format

Play around with the movie, and watch carefully what happens when the balls crash into the blocks. I personally notice two things:

• The superball rebounds farther after it hits the block. It's hard to see this, since you have to account for the perspective.

• The collision with the clay ball lasts a lot longer than the collision with the superball.

We can use the concept of impulse to understand what happens here. The impulse that each ball transfers to the block is equal to the change in momentum of the ball; let's call that change in momentum Dp. That impulse must be equal to the force that the ball exerts on the ball (call that force F) multiplied by the time of the collision (call that dt). So, we have Dp=F x dt, or F=Dp / dt. For the collision with the superball, dt is small and Dp is big (since it rebounds farther we know that the velocity is higher after the collision), so the force is higher compared with the collision with the clay ball. The superball exerts a strong enough force to knock over the block, while the clay ball does not!

If you look even more carefully at the movie, you'll notice something quite neat. Each block really rotates around the edge in contact with the table. In the collision with the clay ball, the torque associated with the force from the ball is not large enough to cause the block to rotate far enough to tip over.

Posted by Prof. Brian DeMarco at 11:07 AM | Permalink

Q: In DR I sat on a stool and held the spinning bicycle wheel. When I flipped over the wheel I started to spin. What was going on??

A: The key point here is that angular momentum (just like linear momentum) is conserved. That means that, if there are no external torques, the angular momentum is constant. No matter when we measure it we will get the same value. We have to be careful to always take all of the angular momentum into account to find that the total angular momentum is conserved.

So, first we had the wheel spinning with some angular momentum. Let's call that L1. With the right hand rule we find that the angular momentum of the wheel is up. You are sitting on the stool, but since you're not spinning you have no angular velocity and thus no angular momentum. So, at the beginning the total angular momentum is just that angular momentum of the wheel, L1 (up).

Then you flipped over the wheel. Since the wheel still has the same angular speed and the same moment of inertia the magnitude of the angular momentum is the same as before, L1. However, since you flipped it over the right hand rule will tell you that the angular momentum points down. Now you are spinning as well, so we will say that your angular momentum is L2. With the right hand rule we find that your angular momentum is up. So, the total angular momentum at the end is L1 (down) + L2 (up)

The conservation of angular momentum says that the total angular momentum can not change (since there are no torques from an external source acting on you or the wheel). So, that means that the angular momentum before and after you flipped the wheel should be the same. That is:

L1(up) = L1(down) + L2(up)

Since down and up are opposite directions we can switch the direction just by adding a negative sign. We rewrite L1 (down) as -L1(up) to get:

L1(up) = -L1(up) + L2(up)

For this equation to be true, it must be the case that:

L2 (up)=2 * L1(up)

Well isn't that interesting! We've just discovered that our angular momentum due to the spinning stool is twice the angular momentum of the wheel.

To explain a bit more conceptually, when you flipped over the wheel you changed its angular momentum. Since the total angular momentum of the system has to be conserved this caused you to spin in the opposite direction with an angular momentum twice as large as the wheel’s (since you have to both zero out the downward angular momentum of the wheel and add more upward angular momentum to equal the original upward angular momentum)

Posted by Rebecca Lamb at 01:37 PM | Permalink

Q: In DR we dropped 2 balls of different masses from the same height and saw that they hit the floor at the same time. This is confusing to me - shouldn't the lighter ball hit first since it has less inertia and the same gravity as the heavier ball?

A: I believe the confusion here is due to a loose use of the word gravity. When we say gravity we may either mean the acceleration due to gravity, which refers to the g=9.8 m/s^2 acceleration experienced by all objects on earth, or we may be referring to the force due to gravity, by which we mean F=mg=weight. When we drop the two balls they both experience the same acceleration due to gravity, 9.8m/s^2, which is why they hit the ground at the same time. However, the force of gravity is different for each ball since F=mg and the masses are different. The less massive ball has a smaller inertia and is easier to accelerate, but it also has a smaller force due to gravity on it. The result is that both balls have the same acceleration due to gravity and thus hit the floor at the same time.

Posted by Rebecca Lamb at 01:18 PM | Permalink