Angular momentum is conserved for systems of objects that are rotating. This is true for figure skaters and students on wheel chairs.
Angular momentum is conserved for systems of objects that are rotating. This is true for figure skaters and students on wheel chairs. (1:02) We agree that when determining rotational directions, we use the right hand rule. (2:56) Rotational kinetic energy can change for rotating objects even if their angular momentum is conserved. (5:44)
The Question of the Day asks: (7:15) If you quadruple the moment of inertia for a rotating object, then what outcome can be expected with respect to the angular speed?
Thank you for listening to The APsolute RecAP: Physics 1 Edition!
(AP is a registered trademark of the College Board and is not affiliated with The APsolute RecAP. Copyright 2021 - The APsolute RecAP, LLC. All rights reserved.)
Website:
EMAIL:
Follow Us:
Hi and welcome to the APsolute RecAP: Physics 1 Edition. Today’s episode will focus on angular momentum or the momentum of rotating objects.
Let’s Zoom out:
Unit 7 – Torque and Rotational Motion
Topic - 7.3 & 7.4
Big Idea – Force Interactions, Change, Conservation
A figure skater spins at center ice with her arms and one leg outstretched. She then pulls her leg and arms in closer to her body and spins much more quickly. How is it that she is able to change her rotational speed so greatly by just bringing her limbs inward?
Let’s Zoom in:
Linear momentum of an object was found by the product of the mass and the velocity of the object. Similarly, the angular momentum can be found by the product of the moment of inertia and the angular speed. The symbol for angular momentum is a capital “L” and the units are (kg*m2)/s. Just like with its linear analogy, angular momentum is conserved as long as there is not a net torque on the system. Multiplying the linear momentum by the radius will result in a conversion to angular momentum. This can be especially useful when an object with linear speed collides with an armature that can rotate.
Back to the figure skater. As she brings her arms inward, she is decreasing her overall radius and therefore her moment of inertia. Since momentum is conserved, as the moment of inertia decreases her angular speed must increase so that the final angular momentum is equal to the initial angular momentum.
One very popular demonstration of angular momentum conservation involves a wheel spinning about a vertical axis of rotation that is held by an individual who is standing or seated on a platform that is free to spin. At first, the person holding the wheel is at rest. BUT, once they flip the wheel so that it is spinning in the opposite direction, the person begins to rotate too. If that wasn’t weird enough, we can actually predict that the person will spin in the same direction as the wheel’s original spin direction. First, we need to agree on spin directions. “What do you mean?” you may ask, the wheel only spins one way, how can there be any disagreement?
From the point of view above the wheel the wheel might be spinning clockwise while from the view underneath the wheel, it would appear to be spinning counterclockwise. Since the two perspectives are different, it makes it hard to agree on rotational direction. Luckily I can give you a hand there… literally... Using my right hand I can wrap my finger in the direction of the wheel’s rotation and my thumb will then point in one and only one direction, downward. We can then both agree that the wheel is spinning with negative momentum and therefore the system of the wheel + person has a negative momentum. Once the wheel is flipped over so that it has positive momentum, the person must begin spinning with negative momentum. The magnitude of the person’s momentum would be twice that of the wheel’s, but the system’s momentum is still equal to the wheel’s initial negative momentum.
Go find a computer chair that can rotate and try it yourself! Grab a spinning wheel, because they are lying all over the place, and give it a spin. Then flip it. See what happens? Well, certainly you can at least find a video online. Enjoy!
But wait, there’s more! Your teacher may or may not have taught you much about the orbiting planets around our sun. It turns out they orbit in ellipses, or ovals. Since the radius is changing, so does the orbital speed throughout a single revolution around the sun. Orbiting masses travel more quickly through space when their orbital radius is smallest and therefore their moment of inertia is smallest. Don’t believe me? Look it up! NASA has some great data on the matter. If the earth’s position was moved suddenly so that its moment of inertia was halved, then the angular speed would be doubled.
Finally, we should probably talk about what is happening to your kinetic energy if you are rotating in a computer chair and pull your arms inward. Since your momentum is conserved and your angular speed increases, then your rotational kinetic energy must also increase. But, the kinetic energy has both speed and inertia in it too, so why isn’t it conserved as well? Because the angular speed increase is squared in the rotational kinetic energy equation and any increase is much larger than the radius’ decrease. If you half your moment of inertia, conservation of momentum states that your angular speed is doubled, and your kinetic energy is then doubled too as a result. From an earlier episode on energy, I pointed out that energy changes are due to work being done on the system. This is work done by your muscles moving the mass of your arms inward. There is no external force, but there is an internal one that is able to increase the system’s energy. Weird… but true.
To Recap…
Angular momentum is conserved for systems of objects that are rotating. We agree that when determining rotational directions, we use the right hand rule. Rotational kinetic energy can change for rotating objects even if their angular momentum is conserved.
Coming up next on the APsolute RecAP Physics 1 Edition, we look at some dynamics topics from earlier in the season and soon we will start testing tips.
Today’s Question of the Day focuses on angular momentum.
Question:
If you quadruple the moment of inertia for a rotating object, then what outcome can be expected with respect to the angular speed?