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### Course: Physics archive > Unit 7

Lesson 2: Torque, moments, and angular momentum- Introduction to torque
- Moments
- Moments (part 2)
- Finding torque for angled forces
- Torque
- Rotational version of Newton's second law
- More on moment of inertia
- Rotational inertia
- Rotational kinetic energy
- Rolling without slipping problems
- Angular momentum
- Constant angular momentum when no net torque
- Angular momentum of an extended object
- Ball hits rod angular momentum example
- Cross product and torque

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# Constant angular momentum when no net torque

Just like how linear momentum is constant when there's no net force, angular momentum is constant where there's no net torque. Created by Sal Khan.

## Want to join the conversation?

- Torque = Force(perpendicular) . Radius ;

If Torque = 0 ; that means either Force(perpendicular) = 0 , or Radius = 0;

Case I : If Force(perpendicular) = 0; that means Acceleration(perpendicular) will be equal to 0; therefore Velocity(perpendicular) won't change . This implies Angular Momentum (L=mvr) won't change. Angular Momentum remains constant.

Case II : If Radius = 0; there is no angular motion, in this case. As it is the simple case where only Linear Momentum (or translational momentum) takes place.

So it always comes out true that if Torque = 0; Change in Angular Momentum will be also equal to 0. i.e. Angular Momentum remains constant when Torque applied is 0.

Am I right?? If not, Please correct myself. Thanks(9 votes)- Torque = 0 when,

1. F = 0

i.e, no force is being applied for rotation to take place

2. r = 0

i.e, the force is being applied on the axis of rotation, which is fixed. Thus, no rotation takes place.

3. θ = 0 or θ = 180

i.e, the force is being applied in the direction of the position vector, which results in zero torque.

Cheers,

Lia(4 votes)

- I did some research on what zero net torque means and found this:

an object that is not rotating has no net torque, but an object rotating at constant angular velocity also has no angular acceleration, and therefore no net torque acting on it .

So does that mean an object with constant velocity has no net force? But there must be some force in order to maintain the constant velocity right?(6 votes)- Newtons first law tells us that an object remains at rest or at a constant velocity unless it is acted upon by a force. (Fricton, Air resistance a.s.o.)

If no friction and air resistance exists then then the object would travel forever in the same direction(!) with the same speed(2 votes)

- So let's pretend that we have a car going off a jump. As the front wheels leave the jump the rear wheels are still on the jump thus forcing the car to undergo angular momentum due to gravity acting on the front of the car with the pivot point being the rear axis. At the different points throughout the flight path....front wheels off the jump and then both sets of wheels off the jump....how will the spinning tires affect the angular momentum of the car? and what if the driver had enough time to throw the car into reverse and start spinning the tires in the opposite direction? Would this stabilize the flight path as the car's initial angular momentum, we will say is in the clockwise direction and then during flight it is now introduced to a counterclockwise angular momentum by throwing the car into reverse?(3 votes)
- nice question

As long as the wheels remain at the same speed of rotation, the angular momentum does not change. In act, the driver only needs to touch the brake pedals or the accelerator pedal to change the inclination of the car.

If he slams his foot on the brakes, this will cause the car to turn forwards since he has reduced the forward spin of the wheels.

In fact, this is how he can control the angle of the car so that it meets parallel to the landing ramp.

Make sense??(2 votes)

- How does the skater change the rate of spinning? What is r referred to in this case?(2 votes)
- r is the radius of the skater's hands away from her body. It's an oversimplification by assuming that all the mass in the skater's arms are in a single point that; i.e. all the mass from the arms are considered to be in the hands. This simplification let's you see the basic relationship between how far the skater's hands are from their body and how fast they spin.(2 votes)

- what is omega?(2 votes)
- if it looks like a w, it is usually angular velocity. (or angular frequency)(1 vote)

- Torque is neither a force, as it doesn't have units of force, nor Work.

Then what exactly is Torque ?(1 vote)- It actually has the same unit as work, N.m, but its a concept very different from work. I like to picture it as the rotational equivalent of force. In the same way, distance and angle, speed and angular speed, mass and moment of inertia are other examples of a mechanical concept and its rotational equivalent. Torque is what act on a system and causes its angular momentum to change.(angular momentum is the rotational equivalent of momentum, its basically a measure of a system's rotation)(3 votes)

- How do you derive the equation L = P r(2 votes)
- To calculate a velocity (in this example) it is being assumed that the string is continuously getting shorter, right?

Otherwise the velocity would be 0 because the mass at the end of the string is always coming back to the same point on the outer rim of the circle.(2 votes) - Is there a name for (torque)*(delta t)? Maybe rotational impulse?(1 vote)
- Well, technically it is called "Angular Impulse", although you could also call it "change in angular momentum."(2 votes)

- Torque * (Detla t) = (Detla L)

Can we call Torque * (Detla t) is a rotational impulse analog to Impulse in translational domain?

are do we have another name for Torque * (Detla t) for this?(1 vote)

## Video transcript

- [Voiceover] So right over here like I've done in previous videos, we have a diagram of a mass. We really should conceptualize
it as a point mass although it doesn't look like a point, it looks like a circle. But imagine a point mass here and it's tethered to something. It's kind of it's tied
to a massless string, a theoretical massless
string right over here. Where functionally a mass of string and it's kind of nailed down. And let's say it's on
a frictionless surface and let's say it has some velocity. And right here we have the
magnitude of its velocity in the direction that is perpendicular to the wire that is holding it, or I guess you can say perpendicular to the radial direction. Now based on that, we've had a definition for angular momentum. The magnitude of angular momentum is going to be equal to the mass, times this velocity, times the radius. And you could also view that and this is kind of always
kind of tying the connections between you know, translational notions and rotational notions. We can see that angular momentum could be the same thing. Well, the mass times its velocity you could do that as the
translational momentum row in the magnitude of translational momentum in this direction times r. So once again, we took
the translational idea, multiplied it by r and we're getting the rotational idea, the angular momentum versus
just the translational one. And we can also think about it in terms of angular velocity. Now this comes straight out of the idea that this v is going
to be equal to omega r. So you do that substitution, you get this right over here. Now, in previous videos we said okay. Like based on this and based on the idea that if torque is held constant then this does not change. You can describe or you could predict the type of behavior, explain the behavior that you might see. The figure skating competition where if someone pulls their
arms in while they're spinning and they're not, you know,
applying anymore torque to spin, and if they pull their arms in, well this thing is going to be constant because there's no torque being applied. Well, their mass isn't going to change so they'll just spin faster. When you do the opposite, the opposite would be happening. But you might have been left a little bit unsatisfied
when we first talked about it because I just told you that. I said, hey look, if torque is, if there's no net torque then angular momentum is constant and then you have this thing happening. But let's dig a little bit deeper and look at the math of it. So you feel good that
that is actually the case. So let's go back, let's go
to the definition of torque. And so the magnitude of torque, I'll focus on magnitudes in this video. The magnitude of torque
is going to be equal to, it's going to be equal to
the magnitude of the force that is in this perpendicular
direction, times r. Times r. Now what is this, this force? Well, this is just going to be equal to the mass force, f equals ma. So this is going to be mass times the acceleration in this direction which we could view as, which we could view as the change in this velocity over time, and we're talking about magnitudes. I guess you could say, it's through the magnitude of velocity
in that direction. And then of course we have times r. Times r. Now if we multiplied both
sides of this times delta t, we get and actually we do
tau in a different color. We do torque in green. We get torque times delta t. Torque times delta t is equal to, is equal to mass times delta v. Delta v in that perpendicular
direction times r. Well, what's this thing going to be? What's this? Well, that's just change
in angular momentum. So this is just going to be
change in angular momentum. And there's a complete analogy to what you might remember from kind of the translational world. The translational world
you have this notion, if you take your force and you multiply it times how long you're applying the force, should do this in a different color. So we multiply it by how long
you are applying the force. So this quantity we often call is impulse. Impulse. That's going to be equal to your change in translational momentum. Your change in translational momentum. And if you have no force then you're not gonna have
any change in momentum or you're gonna have your
conversation of momentum, or it's not gonna change, it's just going to be conserved. And then you can do all sorts of neat, you know, predicting
where your ball might go or whatever else. We have the same analogy here. The analog for force
in the rotational world is torque, it's obviously this force times the kind of radial, times
that radial distance. But if you take torque times how long you're applying that torque, that's going to be your
change in angular momentum. So if you're not applying any torque, if your torque is zero, if your torque is equal to zero, well that means that your delta L is zero. Your angular momentum is not changing or you could say your
angular momentum is constant. So if you don't apply any torque, like once this figure
skater is already spinning and he or she, she's
not pushing to get more, to spin so she's not applying or he's not applying more torque, well then, they're angular
momentum's going to be constant but they can change their rate of spinning by changing r, by changing how far in or out r is, or how far enough the masses are. And obviously I said in the last video, a figure skater is a much
more complicated system than a point mass tethered to, you know, tethered to a rope. You could view a figure skater as kind of being modeled
by a bunch of point masses but hopefully this gives you the idea.