10.2 Physics 6A Angular Momentum

10.2 Physics 6A Angular Momentum - Physics 6A Angular...

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Unformatted text preview: Physics 6A Angular Momentum Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB Angular Momentum Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB This is the rotational equivalent of linear momentum. It quantifies the momentum of a rotating object, or system of objects. If we simply translate the variables, we can get one possible equation: v m p This is the formula for linear momentum Angular Momentum Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB This is the rotational equivalent of linear momentum. It quantifies the momentum of a rotating object, or system of objects. If we simply translate the variables, we can get one possible equation: v m p This is the formula for linear momentum Using I instead of m and instead of v, we get this formula for angular momentum Note that momentum is a vector quantity. We probably will not need to consider that aspect of it in this class, however. If you are curious about what you are missing, check out the section in your book about gyroscopes. Good stuff. I L Angular Momentum Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB r v m L ) r v ( ) r m ( L I L m ass int po 2 Consider the simple case of a small mass (m) tied to a string with radius r. If the mass is swung around in a circle it will have some angular velocity . Notice that it will also have linear velocity (tangential to the circle). The relationship we know for these is v=r . m We can use this idea to find a useful alternate formula for angular momentum. The point mass will have a moment of inertia: 2 r m I Substituting into the standard formula: r We can use this formula when we have a point mass with a given linear velocity at some distance from a pivot point or axis of rotation. Angular Momentum Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB i i f f I I Like linear momentum, angular momentum is conserved . We will use this concept in several types of problems. This is a formula for conservation of angular momentum. Angular Momentum Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB i i f f I I Like linear momentum, angular momentum is conserved . We will use this concept in several types of problems. Also, we should have some formula relating angular momentum to torque (just like we have a formula relating linear momentum to force): This is a formula for conservation of angular momentum. t L This says that any time a torque is applied, there will be a corresponding change in angular momentum....
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10.2 Physics 6A Angular Momentum - Physics 6A Angular...

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