Class Notes 02 December Pick up HW / Turn in HW Today: I = Smiri2 and St = Ia Did you write the general eqns? Did you include FBDs/Vector directions? #1b: Why not use v = r ? #2c: aR = v2/r  aR = 2r, direction? Today: A hard dynamics problem Rotational Work and Energy

Which pulley will allow the same mass to fall in the shortest time? Small, outside one Medium, middle one Large, inside one It depends on other factors. This question uses the crazy rotational inertia demonstrator from Arbor scientific. Answer is C. The larger radius means larger torque, thus greater angular acceleration, thus less time.

Example Calculate the time it takes a mass m to fall a distance y when it is hung from a pulley on the rotational platform at a radius r. The platform has a mass M and radius R. Set up on desk. Use stopwatches to time. With M=705 g, m=55 g, r=2 cm, R=12.7 cm, y0 = 80 cm I get 6.51 s theoretically but usually ___ s experimentally.

Work and Energy KE is due to translation of the center of mass plus rotation about the center of mass. Derive: Does the work-energy principle still hold? That is, does Wnet = DKE? Power: KEROT = ? KEROT = ½ I w2 YES! P = t w (Constant torque)

Example: Combining KEs A hard hollow sphere is rolling without slipping. What fraction of its kinetic energy is due to rotational motion? Why do I need to specify “without slipping”? I = (2/3)MR2 for a hollow sphere, so 2/5 and 3/4. Cylinder: Rot = 1/3 and Trans = 2/3. Hoop: 50%, 50%. Solid sphere is 2/7, 5/7. Solving with kmr2 gives (Rotational fraction) = k/(1+k). KEROT = (2/5)KETotal KETRAN= (3/5)KETotal

The Great Shape Race A sphere, ring, and cylinder all roll down a platform. Which one gets to the bottom first, and why? First of all, does the mass matter? The Radius?

Which will win the race? The ring The disk The sphere All tied Depends on mass and/or radius of each 2016: Turning point failed. But I looked at report for 9:00 class = 3, 0, 5, 1, 3 2015: Turning point failed. But I looked at report for 9:00 class = 3, 1, 4, 0, 0

THE SPHERE! The Great Shape Race No A sphere, ring, and cylinder all roll down a platform. Which one gets to the bottom first, and why? First of all, does the mass matter? The Radius? No THE SPHERE! (Long live the sphere)

Homework Read Chapter 8, section 6-7 Do problems on Worksheet 36 Have a good and safe time at the winter formal.