Your Comments I was doing all right until the checkpoint questions. Just a little bit confusing. can we please have less or even no variable manipulation problems on the next exam... just give me some numbers, I'll happily calculate a number than have to cancel variables... I'm pretty confused about this material. This is the stuff that gave me trouble in AP Physics in high school. I used physics pick-up lines during Unofficial. They worked surprisingly well. I cry, because after I got out of calc 231 for engineers I forgot everything we were taught in that class and I used to be so good at moment of inertia. When is the final exam? I'm really worried about the exam being after spring break. Hula Hoop problem. That is all. Eating Greek food on campus: $ Being part of the Greek system: $$ Learning the Greek alphabet through Physics: Priceless. Buzz and Crunchy were REAL cute! :D I thought this pre lecture was easy. Everything was going perfectly until moment of inertia came along and messed up my happy feeling!! WHY??!!!! Please make moment of inertia easier to understand! The integrations are really confusing... Can we have more explanation in class ? Why did the chicken cross the road? To find Newton on the other side and peck him ruthlessly on the head for inventing physics! (And consequently Calculus too!) 1

Today’s Concepts: a) Rotational Motion b) Moment of Inertia Physics 211 Lecture 14 Today’s Concepts: a) Rotational Motion b) Moment of Inertia

Summary of Rotations Angular velocity w is measured in radians/sec Frequency f is measured in revolutions/sec 1 revolution = 2p radians Period T = 1/f

Dear Professors, Please explain in detail why the direction of positive angular displacement is in the counterclockwise direction. Gladding mentioned that trig was the reasoning briefly but I did not understand what he meant by that.. x y z + q

Centripetal vs Angular Acceleration w Constant a does not mean constant w

Clicker Question A) T = 2 sec B) T = 2p sec C) T = ½ sec A disk spins at 2 revolutions/sec. What is its period? A) T = 2 sec B) T = 2p sec C) T = ½ sec

Clicker Question A) B) C) A disk spins at 2 revolutions/sec. What is its angular velocity? A) B) C) rad/sec rad/sec rad/sec

CheckPoint A wheel which is initially at rest starts to turn with a constant angular acceleration. After 4 seconds it has made 4 complete revolutions. How many revolutions has it made after 8 seconds? A) 8 B) 12 C) 16 a Less than half got this right so lets try again… 8

CheckPoint Response After 4 seconds it has made 4 complete revolutions. How many revolutions has it made after 8 seconds? A) 8 B) 12 C) 16 a A) It makes one revolution per second. B) its not 8 cuz its accelerating so speed is increasing, not sure if its 12 or 16. C) theta=.5alpha(t^2). so doubling t, quadruples revolutions. 9

Calculating Moment of Inertia Depends on rotation axis

CheckPoint A triangular shape is made from identical balls and identical rigid, massless rods as shown. The moment of inertia about the a, b, and c axes is Ia, Ib, and Ic respectively. Which of the following orderings is correct? A) Ia > Ib > Ic B) Ia > Ic > Ib C) Ib > Ia > Ic a b c Only about half got this right so lets try again…

CheckPoint Response Which of the following orderings is correct? a A) Ia > Ib > Ic B) Ia > Ic > Ib C) Ib > Ia > Ic r b r c A) Ia = 8mr^2 Ib = 3mr^2 Ic = 2mr^2 B) Ia = 8mr^2 Ib = 3mr^2 Ic = 4mr^2

Calculation Moment of Inertia “The idea that a spherical shell has a higher moment of inertia doesn't really make sense to me because it has less mass than a solid sphere.” Bigger when the mass is further out

Clicker Question In both cases shown below a hula hoop with mass M and radius R is spun with the same angular velocity about a vertical axis through its center. In Case 1 the plane of the hoop is parallel to the floor and in Case 2 it is perpendicular. In which case does the spinning hoop have the most kinetic energy? A) Case 1 B) Case 2 C) Same w R Case 2 Case 1 Less than half got this right so lets try again… 14

w In which case does the spinning hoop have the most kinetic energy? A) Case 1 B) Case 2 C) Same w R Case 2 Case 1 A) Case 1 because more mass is farther away from the line about which it is rotating. C) All you did was turn the hoop on it's side which will have no effect on the kinetic energy. 15

Clicker Question A mass M is uniformly distributed over the length L of a thin rod. The mass inside a short element dx is given by: A) B) C) D) dx x L M

Clicker Question A mass M is uniformly distributed over the length L of a thin rod. The contribution to the rod’s moment of inertia about an axis through its center provided by element dx is given by: A) B) C) axis dx x L M

Clicker Question A disk has a radius R. The area of a thin ring inside the disk with radius r and thickness dr is: A) B) C) r dr

(i) (ii) (iii) Using (ii) Using (i)

(iv) (v) Use (iv) Use (v) 20

(vi) (vii) (viii) (ix) Use (viii) Use (ix) 21

(vi) (vii) (viii) (ix) Use (vii) Use (vi) 22