1. Announcements CAPA #11 due this Friday at 10 pm Reading: Finish Chapter 8, Start Chapter 9.1-9.4 Section – this week Lab #4: Rotations Midterm Exam #3 on Tuesday November 8 th, 2011  details given in class on Wednesday  practice exam and solutions on CULearn  formula sheet to be posted on web page Fraction of all clicker questions answered posted on CULearn. Email me with your clicker ID, name, student ID if you believe it is incorrect.

2. Which has a larger moment of inertia? A)I A > I B B) I A < I B C) I A = I B D) Impossible to tell. Clicker QuestionRoom Frequency BA Consider two masses each of size 2m at the ends of a light rod of length L with an axis of rotation through the center of the rod. The rod is doubled in length and the masses are halved.

3. A bar has four forces, all of the same magnitude, exerted on it, as shown. What is the sign of the net torque about the axis of rotation? Use the sign convention shown. Clicker QuestionRoom Frequency BA A) torque is zero B) positive (+) C) negative (–)  net = + (F)(L) + (F)(L/2) + (F)(L/2) – (F)(L) = +FL

4. Rotational Kinetic Energy Does this object have translational kinetic energy? No, zero net translational velocity of the object. However, there is motion of each piece of the object and thus there must be kinetic energy. Each piece of the donut has a velocity v =  r. KE = ½ mv 2 = ½ m (  r) 2 KE = ½ I  2 Rotational KE

5. Rolling Kinetic Energy TranslationRotation KE (total)= KE (translation) + KE (rotation) KE total = ½ mv 2 + ½ I  2 Both pieces in units of Joules. * Rolling without slipping means v =  r. One revolution  =2  leads to displacement of 2  r

6. Which object has the largest total kinetic energy at the bottom of the ramp? A) Sphere B) Disk C) HoopD) All the same. Clicker QuestionRoom Frequency BA M All have the same total KE.

7. M

8. M Sphere

9. Which has the greater speed at the bottom of the ramp, the sphere that rolls down the ramp or a block of the same mass that slides down the ramp? (Assume sliding friction is negligible) A) BlockB) SphereC) Both the same Clicker QuestionRoom Frequency BA Block

10. Sphere : Hoop: Disk: Who wins the race to the bottom…… sphere, disk, hoop? Smallest moment of inertia I will have the largest translational velocity at the bottom.

11. Demonstration

12. Which object will go furthest up the incline? A) PuckB) DiskC) HoopD) Same height. The hoop has the largest moment of inertia, and therefore the highest total kinetic energy. H Clicker QuestionRoom Frequency BA

13. Recall: Momentum p = mvL = Iω Angular momentum Relation to force F = Δp/Δtτ = ΔL/Δt Relation to torque No external force Δp = 0ΔL = 0 No external torque (momentum is conserved)(angular momentum is conserved) I i ω i = I f ω f Conservation of Angular Momentum L i = L f

14. I i large ω i small I i small ω i large By changing the distribution of mass, the moment of inertia is changed. By conservation of angular momentum, the angular velocity is therefore modified. Conservation of L:

15. I 1 large ω 1 small By changing the distribution of mass, the moment of inertia is changed. By conservation of angular momentum, the angular velocity is therefore modified. Conservation of L: I 2 small ω 2 large I 3 large ω 3 small

16. Hoberman Sphere