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Announcements

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

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Announcements

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  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 8th, 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. Clicker Question Room 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. Which has a larger moment of inertia? IA> IB B) IA < IB C) IA = IB D) Impossible to tell.

  3. Clicker Question Room Frequency BA 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. A) torque is zero B) positive (+) C) negative (–) tnet = + (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 = w r. KE = ½ mv2 = ½ m (w r)2 KE = ½ I w2 Rotational KE

  5. Rolling Kinetic Energy Translation Rotation KE (total) = KE (translation) + KE (rotation) KEtotal = ½ mv2 + ½ I w2 Both pieces in units of Joules. * Rolling without slipping means v = w r. One revolution Dq=2p leads to displacement of 2pr

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

  7. M

  8. M Sphere

  9. Clicker Question Room Frequency BA 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) Block B) Sphere C) Both the same Block

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

  11. Demonstration

  12. Clicker Question Room Frequency BA H Which object will go furthest up the incline? A) Puck B) Disk C) Hoop D) Same height. The hoop has the largest moment of inertia, and therefore the highest total kinetic energy.

  13. Conservation of Angular Momentum Recall: Momentum p = mvL = IωAngular momentum Relation to force F = Δp/Δtτ = ΔL/ΔtRelation to torque No external force Δp= 0 ΔL = 0No external torque (momentum is conserved) (angular momentum is conserved) Li= Lf Iiωi = Ifωf

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

  15. 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: I1large ω1small I2small ω2large I3large ω3small

  16. Hoberman Sphere

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