Can you please explain Angular momentum?

[Nivvedan]

How can angular momentum be conceptually thought of? I find it easy to visualize linear momentum as how difficult it is to stop a body possessing that momentum or the extent of damage that body causes on hitting another body. But I find it very difficult to conceptually visualize angular momentum. I can do it mathematically but what exactly is it?

Can you please help me there? Please explain in simple terms so that I can understand easily.

[Mr Skeptic]

It's basically spin. Angular momentum changes when you apply torque to a system.

[Klaynos]

As you said with liniar momentum being how difficult it is to stop a body moving in a straight line, angular momentum is how difficult (directly related to the strength of the torque required) it is to stop something moving in it's curved path.

[D H]

Neither of these is quite correct. The first reply, "spin", is talking about angular velocity, not angular momentum. The second, "curved path", concept is not quite correct either. A wheel rotating on a fixed axis is not moving, but it is spinning. The analogy in the second post is good: Angular momentum is to angular velocity as linear momentum is to linear velocity. Just as force changes a body's linear momentum, torque changes a body's angular momentum.

 

The reason you are confused is because rotational behavior is a lot more confusing that linear behavior.

[Mr Skeptic]

Yes, angular momentum is the product of rotational inertia and angular velocity just as momentum is the product of inertia and velocity. The rotational inertia depends on where your axis of rotation is (unlike regular inertia). The masses in the system need not be connected to each other; an orbital system has angular momentum. Also, though it is fairly popular to use the center of mass as the axis of rotation, you can use whatever axis of rotation you feel like. So as D H said, it is more confusing.

[D H]

Its also more confusing because while linear momentum and linear velocity are always coaligned, the same is not the case for rotational behavior. Mass is a scalar while the inertia tensor is rank 2 tensor.

 

This rank 2 tensor is constant in the rotating body frame for a rotating solid body. Another source of complexity: The inertia tensor is a time-varying quantity in the inertial frame. There are two ways to address this problem:

• Express the rotational equations of motion in the rotating body frame, which requires the addition of fictitious torques to the equations of motion.
  
• Express the rotational equations of motion in the inertial frame, which requires expressing the inertia tensor in the inertial frame (yech) and computing the derivative of the inertia tensor as seen by an inertial observer (YECH!).

The latter approach is nontenable. The 'natural' frame in which to express rotational behavior is the rotating body frame. Physics students are not exposed to the real wonders of rotational behavior until they hit their junior year or higher. Even Euler's equations are a simplified form of the body frame rotational equations of motion.

[pioneer]

Linear momentum requires a force to act, parallel to the motion, to change the momentum. While angular momentum requires torque or force X distance to change the angular momentum. The distance variable, added perpendicular to the force, is needed since the angular momentum is not just velocity, but also acceleration. The acceleration keeps the velocity moving in a circle. This force is not a static linear force but a radial force, or a linear force that is constanting changing direction.

 

The net result is angular momentum has energy in both velocity and acceleration, while linear momentum only has energy in velocity. For example, if we could overcome the gravitational force using force/energy, the earth would be released from the sun, having only linear momentum.

[theCPE]

How can angular momentum be conceptually thought of? I find it easy to visualize linear momentum as how difficult it is to stop a body possessing that momentum or the extent of damage that body causes on hitting another body. But I find it very difficult to conceptually visualize angular momentum.

 

As a kid I would get a kick out of flipping my bicycle over on its handle bar and seat, peddling the wheel up to a fast speed and then trying to stop the tire with my foot (not in spokes, on tire).

 

Great example of angular momentum, you can't just grab the tire and expect it to stop (great way to lose a finger, hand, or depending on how young an arm!)

 

I also liked playing around with gyroscopes, small example of angular momentum (and some other concepts too).

 

Once you get an idea of what angular momentum "looks" like it is pretty easy to understand it and relate it to linear momentum.

[swansont]

Linear momentum requires a force to act, parallel to the motion, to change the momentum.

 

I think you'll find that any force will change the momentum, by definition. A parallel force will increase the magnitude without changing the direction of the vector, which is a special case.