Angular Momentum - lecture 11 PDF

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lecture 11...

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Angular Momentum Angular momentum is the rotational inertia of an object multiplied by its angular velocity

Similar to linear momentum, this is the quantity of rotational motion in the object

Angular momentum is a measure of how hard it will be to stop the object rotating

Remember the radius of gyration and how we use it to find the rotational inertia

So angular momentum is also,

But how does angular momentum relate to torque?

But

so if we multiply by I, we get

so that,

And taking delta t to be infinitesimally small,

Therefore, torque is the time rate of change of angular momentum

Just like a torque, angular momentum is a vector

1. 2. 3. 4.

Magnitude is rotational inertia times angular speed Direction is the axis of rotation Point of application is the axis of rotation Line of action is along the axis of rotation

Angular Impulse Lets go back to one of the equations we derived:

And rearrange it a bit:

The quantity of torque times time is called angular impulse One last rearrangement

So if you are rotating with angular momentum L1 and an angular impulse is applied to you for an amount of time delta t, then you end up with new angular momentum L2.

Angular Momentum To create angular momentum in an object, such as this tennis racket, a torque must be applied. In this case at the shoulder Angular momentum of racket and arm produced by shoulder muscle torque

Once airborne you angular momentum is constant since you have no reaction forces with which to create a torque about your center of mass Angular momentum of the body produced by the reaction force of the horse x dperpedicular to vaulter’s push of

Linear and Angular Momentum An object can have both linear and angular momentum at the same time

Creating Angular Momentum

Stability of Angular Momentum When an object is rotating about an axis, with angular momentum, it has gyroscopic stability What this means is that it requires a torque to change the direction of the axis of rotation Angular momentum vector will always point in the same direction when no external torques

Conservation of Angular Momentum It is a diver’s control to change their rotational inertia, I, by changing the orientation of their body segments Remember, I is large when mass is far from the axis of rotation I is small when we are tucked in tight and mass is close to the axis of rotation This way the diver controls the angular speed. Faster in tuck, slower when laid out.

Conservation of Angular Momentum The whole time the angular momentum is constant

Since angular momentum is a vector, then it can be broken up into components Each component is a rotation about an axis...