Angular Mechanics Angular Momentum Contents Review Linear and

Angular Mechanics - Angular Momentum Contents: • Review • Linear and angular Qtys • Angular vs. Linear Formulas • Angular Momentum • Example | Whiteboard • Conservation of Angular Momentum • Example | Whiteboard

Angular Mechanics - Angular Quantities Linear: (m) s (m/s) u (m/s) v (m/s/s) a (s) t (N) F (kg) m (kgm/s) p Angular: - Angle (Radians) o - Initial angular velocity (Rad/s) - Final angular velocity (Rad/s) - Angular acceleration (Rad/s/s) t - Uh, time (s) - Torque I - Moment of inertia L - Angular momentum TOC

Linear: s/ t = v v/ t = a u + at = v ut + 1/2 at 2 = s u 2 + 2 as = v 2 (u + v)t/2 = s ma = F 1/ mv 2 = E 2 kin Fs = W mv = p Angular: = / t* = o + t = ot + 1/2 t 2 2 = o 2 + 2 = ( o + )t/2* = I Ek rot = 1/2 I 2 W = * L = I *Not in data packet TOC

Angular Mechanics – Conservation of angular momentum Angular momentum is a vector. (It has a Magnitude and a Direction) Magnitude - I Direction – Orientation of axis TOC

Conservation of Magnitude: • Ballerina Pulls in arms • I 1 1 = I 2 2 TOC

Example: A merry go round is a 210 kg 2. 56 m radius uniform cylinder. Three 60. 0 kg children are initially at the edge, and the MGR is initially moving at 5. 4 rad/s. What is the resulting angular velocity if they move to within. 50 m of the center? Whiteboards from momentum TOC

Conservation of Magnitude: • Planets around sun • Contracting Nebula | IP Demo • Crazy Merry go round tricks • Motorcycle • On a jump • Revving • People jumping from cliffs • Aiming the Hubble • Demo stopping the gyroscope • Bicycles • Demo hanging gyro • Demo Turning a gyro over TOC