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## AP®︎/College Physics 1

### Course: AP®︎/College Physics 1>Unit 5

Lesson 5: Angular momentum and torque

# Angular momentum

Introducing angular momentum conceptually starting from linear momentum. Also covers some real-life examples. Created by Sal Khan.

## Want to join the conversation?

• At , perhaps they use "L" because it resembles the sign "∠" used to represent angles.

http://www.rapidtables.com/math/symbols/Geometry_Symbols.htm •  Nice one:

or maybe as sal pointed out:
- A was already used for "Area/magnetic vector potential/amplitude".
- a for acceleration.
- M for "moment of force/magnetization".

And L was simply used because of the sound of the latin word "Angulus".

or:

The scientist who is responsible for the naming just looked out the window and the first thing he saw started with the letter L.

We will probably never know.
• Is there a video that takes into consideration the moment of inertia. • I have a question :
If radius decreases then angular velocity or speed increases OK!
Now if something was travelling at a speed v1 before decrease in radius and v2 after decrease in radius then we know v2>v1 right if no force was applied to it.
so kinetic energy before was 1/2 mass v1^2
and after 1/2 mass v2^2
since v2>v1
kinetic energy after is greater than before.
So my question:
Where does the energy came from, isn't that breaking law of conservation of energy??
Thanks!! • Actually, the translational speed does not stay the same, considering that no torque was exerted on the system. What remains constant is the angular momentum, mvr. So, since the mass doesn't change, v.r is constant, thus decreasing the radius does increase the speed.
The extra kinetic energy comes from the force you exerted to pull the object from r1 to r2.
The net force exerted on the object at every moment, if we're decreasing the radius very slowly(we don't need to, its just to make it simpler), is mv²/r, the centripetal force.
So, the work done will be
W = -∫F.dr (from r1 to r2) =
-∫mv²dr/r =
-m.∫(v1.r1)².dr/r³ (from the condition v.r is constant, we have v.r =v1.r1 ---> v² = v1²r1²/r²)
= -m.(v1.r1)².[-1/2r2² + 1/2r1²]
= mv1².[(r1² - r2²)/r2²]/2
Which should be equal to the total change in energy.
ΔE = mv2²/2 - mv1²/2
= mv1²r1²/2r2² - mv1²./2 (here, I used v2r2 = v1r1)
= mv1².[(r1² - r2²)/r2²]/2
= W
So, all the extra energy comes from the work exerted by the pulling force.
• After sal said that torque is constant. But torque= Force x radius so if the radius decreases the torque should change right? • Does boomerang turns because of angular momentum? • What is the difference between angular momentum and angular velocity
(1 vote) • Sal said that L=mvr, where v is the magnitude of the perpendicular component of the velocity, but he also said L is a vector quantity. How is this so? • Two questions: 1) Why don't we just have w NOT be in radians. Then all of our formulas could be simpeler. Maybe we could define it as orbital velocity or something? And 2) a read somewhere that orbital velocity doesn't actually limit to tangential velocity, so v does not equal rw. Is this accurate? • The two questions are the same. The reason we use radians for angular velocity is because in that case, the unit radians falls straight out of the mathematics and r*w, when we write angular velocity in radians, is equal to v. If we were to write angular velocity in rotations per unit time rather than radians per unit time, then they would not be the same.
• what is tangential velocity and why it is perpendicular to radius in above video? • To elaborate on that, any 2D vector can be broken down into 1D components of that vecotor. Typically the vectors we choose to use are vectors that are perpendicular to each other because that makes things simplest. For instance, a vector pointing North-East can be considered as the sum of two equal magnitude vectors, one pointing North and the other East.

When considering circular motion, it's often easier to decompose vectors into tangential (perpendicular to the radius) and radial (along the direction of the radius). This is because if the components were defined in terms of cartesian coordinates (e.g. X and Y or North/South and East/West) the velocity of a spinning object would be constantly changing as the object moves around the circle. By discussing tangential and radial velocity, the analysis becomes much simpler. (typically, tangential velocity is constant and radial velocity is zero).
• Let's say we have a wooden plank sliding at a speed of 5 m/s. The mass of the rod is 1 kg, and its center of mass is the exact center of the plank. The plank hits a stationary object 0.5 meters away from the center of mass. How fast does it rotate?

L = Pr
mr²ω = mvr
rω = v
0.5ω = 5 