Rotational Kinematics Intro D Taylor 2013 Non-Basic Stuff Inertia: Mass, m, is measure of it regularly. Inertia is the property that resists a change in motion. I So, ROTATIONAL Inertia, I, is the property of an object that resists a change in its rotational state. Non-Basic Stuff Rotasional Inertia: Mathematical Definition : Non-Basic Stuff Inertia: SHAPE MATTERS ! Non-Basic Stuff Solid Disc Non-Basic Stuff Hollow Disc Non-Basic Stuff Solid Sphere Non-Basic Stuff Bar at center Non-Basic Stuff Bar at end Non-Basic Stuff Torque : Rotational F Figure A large grindstone is given a spin by a person grasping its outer edge. Rotational KE Roll SOLID Disc Down Ramp? Roll HOLLOW Disc Down Ramp? Roll SOLID BALL Down Ramp? L Finally; Angular Momentum (L) L L MUST be conserved! Figure The Solar System coalesced from a cloud of gas and dust that was originally rotating. The orbital motions and spins of the planets are in the same direction as the original spin and conserve the angular momentum of the parent cloud. Figure Figure (a) shows a disk is rotating counterclockwise when viewed from above. Figure (b) shows the right-hand rule. The direction of angular velocity size andangular momentum L are defined to be the direction in which the thumb of your right hand points when you curl your fingers in the direction of the disks rotation as shown. Figure In figure (a), the torque is perpendicular to the plane formed by r and F and is the direction your right thumb would point to if you curled your fingers in the direction of F. Figure (b) shows that the direction of the torque is the same as that of the angular momentum it produces. Figure The image shows a view down the barrel of a cannon, emphasizing its rifling. Rifling in the barrel of a canon causes the projectile to spin just as is the case for rifles (hence the name for the grooves in the barrel). (credit: Elsie esq., Flickr) Satellite Orbit vAvA vBvB Spinning Skater? Why? Hoberman! Rotational Dynamics via Hollywood? HA Core #s Inner Radius = 1200 km Outer Radius = 3470 km T both = 24 hrs Mass inner = 0.10 M earth Mass outer = 0.31M earth Find Ke rot of core! 500,000,000,000,000,000,000,000,000,000,000 J 500 Nonillion 5x10 32 J 5x10 32 J Analogies? About the amount of energy the entire Sun emits in 100 seconds. That's a whole lot of energy. five trillion one megaton bombs If it doesn't sound like much, let's convert it to megatons: it's the equivalent energy of five trillion one megaton bombs 5,000,000,000,000 MILLION TONS TNT! going off at once. That is comfortably more than the entire arsenal of the planet. 500 million times In fact, it's about 500 million times the explosive energy of every single nuclear weapon* on the Earth. *That we know of