Unit 4 Summary

Conservation of Angular Momentum

When an ice skater goes into a spin, she speeds up rapidly. This happens because of the Conservation of Angular Momentum. The former momentum formula still applies here: p before=p after, except the object is rotating. When her arms are extended, it slows her down because her mass is not all close to her axis of rotation. When she changes her spin and pulls her arms in, that moves more of her mass to the center and increases her rotational velocity.

Rotational and Tangential Velocity

When you're riding a train and feel a slight shift horizontally, that is because of rotational and tangential velocities. Train wheels are designed especially to keep themselves on the track, and they actually self correct because of physics. The wheels have a tapered design where they are smaller on the exterior and larger on the interior. The two sides of the wheel make the same number of revolutions in a certain amount of time (rotational velocity), but the interior side of the wheel has a higher tangential velocity because it has less time to make a larger rotation because it has a larger circumference.

 

Rotational Inertia

As you can see in this picture, a hollow disk and a solid disk are going to race down a ramp. Initially, I thought that the hollow disk would win because it has less mass but that is not the case. Rotational inertia is the willingness an object has to rotate. An object with higher rotational inertia is harder to rotate. The closer the mass is to the axis of rotation, the lower rotational inertia it has. Likewise, the hollow disk will have a higher rotational inertia because its mass is distributed to the outside of the object. Due to these properties, the solid disk will win the race because its mass is distributed evenly and around the axis of rotation.

Torque

As we know, torque = force x lever arm. The force can either be gravity, or an added weight onto the system. The lever arm is the distance from the axis of rotation to where the weight falls. When one lever arm is created, another one is too, so we use the formula (f)(lever arm)=(f)(lever arm) to ensure that the two sides are balanced. Because f x lever arm = torque, we can say that the clockwise torque is equal to the counterclockwise torque. In the example below, adding a rope to the end of a wrench does not increase the lever arm. It may increase the force because you get a better stance, but it does not increase the distance from the axis of rotation to the point where force is being applied.

Center of Mass/Gravity

As a kid when my family and I traveled to Italy, we went to visit the leaning tower of Pisa and I was appalled by it’s slant and how it doesn’t fall over. This is because its center of gravity has not yet fallen over the alignment of its base of support. Two problems that contribute to the falling of an object are a high center of gravity and a narrow base of support. In wrestling, the players do just the opposite to stay standing. They widen their base of support and lower their center of gravity so that there is more distance in their base of support so they are less likely to fall over when wrestled with.

Centripetal/Centrifugal Force

The word “centripetal” seems daunting because it is used in really advanced math, but it is pretty simple. Centripetal means center-seeking. So a centripetal force is a force that acts on an object, forcing it inwards towards the axis of rotation (the center of an object). If when a car makes a sharp turn, the centripetal force pushes you towards the center, but why do you fly the other way? This is because of centrifugal force. It isn’t actually a force, but rather the reaction to centripetal force.