Tinkering With Inertia
Newton's first law of motion describes inertia: a body a rest will stay at rest, and a body in motion will stay in motion in a straight line at a constant speed unless either is acted upon by an outside force. We read about inertia in the Dynamics section of the Usborne Science Encyclopedia (pg. 122.) This is not just a linear property, but a rotational one as well.
We used Tinker Toys to explore rotational inertia. (You could also do this with clay and dowels if you want.)
Ds#3 is holding two Tinker Toy configurations that use the exact same pieces. I had the boys hold each one in the center and twist it back and forth, making the top and bottom swing back and forth like a pendulum. I asked which would be easier to swing; they thought the one with the weights at the ends would be. They were surprised!
The farther the weight, the greater the inertia, so the harder it is to move.
Ds#2 is showing our next experiment. Here I asked the boys to try and balance this structure on their palm. They tried it with the weight closer to their palms...
...and with the weight farther away from their palm. They predicted the first position would be easier to balance.
They were surprised again!
As in the first experiment, the farther the weight, the greater the inertia, so the harder it is to move.
Next Ds#1 is demonstrating another structure that I had them balance on one finger. You see that his finger is at the center of the structure with equal weights in each end.
I asked what they thought would happen if I moved the weight in on one side. Ds#2 thought the side with the closer weight would be heavier, and Ds#1 thought the other side would be heavier. The toy fell towards the weight that was farther away. In the picture, Ds#1 shows that he had to move his finger so that it was midway between the weights, not the middle of the bar, to balance the structure.
Here gravity is acting on the mass creating a force; rotational force is called torque, which is a force exerted at a distance from the axis of rotation. The longer the arm, the greater the torque.
I then showed them how this all relates to something common: a seesaw. I asked which end of the seesaw they would rather have to lift. At first they thought the side with the closer weight, but after a moment they changed their mind.
This time they were right!
Just like the second experiment, a fulcrum is the axis of rotation, so the longer the arm the greater the gravitational torque.
We then played with the Torque and Moment of Inertia Gizmo. Torque equals the force multiplied by the distance from the fulcrum:
T = r F
Even without knowing actual values, you can see that the farther the weight is (the greater r is) then the greater the torque is. If you have to lift a weight using a fulcrum, like a seesaw or a pulley, you certainly don't want the short end of the stick!
Another example of this is when skaters spin. With their arms out, the center of mass is farther from the center and the spin is slower than when they bring their arms close to their bodies. This is also why two balls of the same mass but different size will roll down an inclined plane at different rates. The smaller ball rolls faster since less energy has to be spent to overcome the rotational inertia.
For an advanced discussion, see Fizzics Fizzle.