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Physics 101: Lecture 13 Rotational Kinetic Energy and Inertia

Exam II. Physics 101: Lecture 13 Rotational Kinetic Energy and Inertia. SAPHA: South Asian Pre-Health Association-General Body Meeting Who : Pre-Health Students (Pre-Med, Pre-Dent, Pre-Pharm , etc.) When : Thursday March 4, 2010 at 6:00 P.M. Where : Noyes 165

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Physics 101: Lecture 13 Rotational Kinetic Energy and Inertia

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  1. Exam II Physics 101: Lecture 13Rotational Kinetic Energy and Inertia

  2. SAPHA: South Asian Pre-Health Association-General Body Meeting Who: Pre-Health Students (Pre-Med, Pre-Dent, Pre-Pharm , etc.) When: Thursday March 4, 2010 at 6:00 P.M. Where: Noyes 165 Why: Come join us for a roundtable discussion about why students chose to go into their respective health related fields! Refreshments will be served!

  3. SP10 Exam 1 Results Best questions 5. Ave = 99% 6. Ave = 97% 10. Ave = 93% Worst questions: 12. Ave = 18% 20. Ave = 34% 16. Ave = 40% Q. Numbers are for form A.

  4. SP09 Exam 1 Results Best questions 17. Ave = 97% 21. Ave = 91% 5. Ave = 90% Worst questions: 18. Ave = 18% 9. Ave = 27% 8. Ave = 29% Q. Numbers are for form A.

  5. Overview of Semester • Newton’s Laws • S F = m a • Work-Energy • S F = m a multiply both sides by d • S W = DKE Energy is “conserved” • Useful when know Work done by forces • Impulse-Momentum • S F = m a multiply both sides by Dt • S I = Dp Momentum is “conserved” • Useful when know about EXTERNAL forces • Works in each direction independently

  6. Linear and Angular Motion Linear Angular Displacement x q Velocity v w Acceleration a a Inertia m I KE ½ m v2 N2L F=ma Momentum p = mv Today!

  7. Comment on axes and sign(i.e. what is positive and negative) Whenever we talk about rotation, it is implied that there is a rotation “axis”. This is usually called the “z” axis (we usually omit the z subscript for simplicity). Counter-clockwise (increasing q) is usuallycalled positive. Clockwise (decreasing q) is usuallycalled negative. +w z

  8. Energy ACT • When the bucket reaches the bottom, it’s potential energy has decreased by an amount mgh. Where has this energy gone? A) Kinetic Energy of bucket B) Kinetic Energy of flywheel C) Both 1 and 2. At bottom, bucket has zero velocity, energy must be in flywheel!

  9. Rotational Kinetic Energy • Consider a mass M on the end of a string being spun around in a circle with radius r and angular frequency w • Mass has speed v = w r • Mass has kinetic energy • K = ½ M v2 • = ½ M w2 r2 • Rotational Kinetic Energy is energy due to circular motion of object. M

  10. Rotational Inertia I • Tells how much “work” is required to get object spinning. Just like mass tells you how much “work” is required to get object moving. • Ktran = ½ m v2 Linear Motion • Krot = ½ I w2 Rotational Motion • I =S miri2 (units kg m2) • Note! Rotational Inertia (or “Moment of Inertia”) depends on what you are spinning about (basically the ri in the equation).

  11. Rotational Inertia Table • For objects with finite number of masses, use I = S m r2. For “continuous” objects, use table below (p. 263 of book).

  12. A B Merry Go Round Four kids (mass m) are riding on a (light) merry-go-round rotating with angular velocity w=3 rad/s. In case A the kids are near the center (r=1.5 m), in case B they are near the edge (r=3 m). Compare the kinetic energy of the kids on the two rides. KE = 4 x ½ m v2 = 4 x ½ m w r2 = ½ I w2 Where I = 4 m r2 Further mass is from axis of rotation, greater KE it has. A) KA > KB B) KA = KB C) KA < KB

  13. Contest!

  14. Inertia Rods Two batons have equal mass and length. Which will be “easier” to spin A) Mass on ends B) Same C) Mass in center I = S m r2 Further mass is from axis of rotation, greater moment of inertia (harder to spin)

  15. Preflight: Rolling Race (Hoop vs Cylinder) A solid and hollow cylinder of equal mass roll down a ramp with height h. Which has greatest KE at bottom? A) Solid B) Hollow C) Same 27% 22% 51% “Both start with same PE so they both end with same KE.”

  16. I = ½ MR2 I = MR2 Preflight: Rolling Race (Hoop vs Cylinder) A solid and hollow cylinder of equal mass roll down a ramp with height h. Which has greatest speed at the bottom of the ramp? A) Solid B) Hollow C) Same 41% 18% 40% “The hollow cylinder has a larger moment of inertia so it takes more energy to get it rolling. The solid cylinder takes less energy so it rolls faster and gets there first.”

  17. Main Ideas • Rotating objects have kinetic energy • KE = ½ I w2 • Moment of Inertia I = S mr2 • Depends on Mass • Depends on axis of rotation • Energy is conserved but need to include rotational energy too: Krot = ½ I w2

  18. Massless Pulley Example Consider the two masses connected by a pulley as shown. Use conservation of energy to calculate the speed of the blocks after m2 has dropped a distance h. Assume the pulley is massless. Note: Tension does positive work on 1 and negative work on 2. Net work (on 1 and 2) by tension is ZERO. 37

  19. Massive Pulley Act Consider the two masses connected by a pulley as shown. If the pulley is massive, after m2 drops a distance h, the blocks will be moving A) faster than B) the same speed as C) slower than if it was a massless pulley Slower because some energy goes into spinning pulley! 45

  20. Summary • Rotational Kinetic Energy Krot = ½ I w2 • Rotational Inertia I = S miri2 • Energy Still Conserved! • Practice Problems Ch. 8: 1,3,5,9 50

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