1 / 11

Angular Momentum

Angular Momentum. Moment of Momentum . To continue the analysis of rotational motion, we must also extend the idea of momentum. Define an angular momentum L . Based on the momentum p = mv Includes a lever arm Follows the rules for torque. p. r. Momentum Cross Product .

Mia_John
Download Presentation

Angular Momentum

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Angular Momentum

  2. Moment of Momentum • To continue the analysis of rotational motion, we must also extend the idea of momentum. • Define an angular momentum L. • Based on the momentum p = mv • Includes a lever arm • Follows the rules for torque p r

  3. Momentum Cross Product • Angular momentum is a vector. • Vector cross product of the lever arm and momentum. • Direction follows the right-hand rule • Magnitude from sine rule L p r

  4. Law of Angular Inertia • The time derivative of angular momentum vector is the net torque vector. • By the law of reaction, all internal torques come in canceling pairs. • Add external torques

  5. Applying Torque • An external torque changes angular momentum. • dL/dt= t L L+rpsinq w w p

  6. A child of 180 N runs at 4.5 m/s and hops on the edge of a merry-go-round with radius 2.0 m. If the motion is perpendicular to the radius, what is angular momentum? The child starts with linear momentum. W = mg, m = W/g = 18 kg. p = mv = 81 kg m/s At right angles, all the linear momentum contributes. L = rp = 160 kg m2/s The torque is due to the friction at contact. Starting the Ride m r

  7. Spinning Mass • The moment of inertia is the analog of mass for rotational motion. • The analog for angular momentum would be: w

  8. A child of 180 N runs at 3.0 m/s and hops on the edge of a merry-go-round with radius 2.0 m and mass of 160 kg. What is the period of rotation? The moment of inertia and the angular momentum for the child on the ride was found before. I = Id + Ic =390 kg m2 L = rp = 160 kg m2/s The period is related to the angular velocity. L = Iw = I(2p/T) T= 2p I/ L = 15 s Initial Spin m M r

  9. Single Axis Rotation • An axis of rotation that is fixed in direction gives a single axis rotation. • Simplest case has the axis through the center of mass • Angular momentum vector is parallel to the angular velocity L w

  10. Limitations • There are limitations to the relationship between angular momentum and angular velocity. • Moving axis of rotation • Asymmetric axis of rotation • Angular momentum and angular velocity can have different directions. p L r

  11. Angular Momentum Vector • The vector form of the law of rotational action is generalized to use angular momentum vectors. • Correct for all axes • Correct for changes in direction as well as angular velocity next

More Related