0. comprehensive momentum/impulse notes

1. livestream

2. Unit 6 Notes - Rotational Mechanics

3. discussed center of mass (this time focus is on continuous mass distributions) ... notes here

4. discussed another note packet regarding center of mass (and also discussing moment of inertia) ... note packet here (through slide 32)

5. reviewed the difference between finding the center of mass and the rotational (or moment of) inertia

6. note the method of calculating moment of inertia:

a. always start with the integral of r^2 dm

b. write dm=(lambda)dx for lines of mass ... write dm=(sigma)dA for areas of mass ... and write dm=(rho)dV for volumes of mass

c. sub in for lambda=Mtot/L ... or sigma=Mtot/A ... or rho=Mtot/V

d. figure out an expression for dx, or dA, or dV

e. sub completed expression for dm back into integral of r^2 dm and do integral

7. worked out moments of inertia for stick (about end), stick (about middle), hoop, and disk.

8. discussed calculating the rotational energy of a stick whirled about its end; about its middle....given omega, the mass and the length of the stick

9. Help Video on Rotational Inertia

10. Screencastify introducing the rotational inertia quantity

11. Today's Recording

0. comprehensive momentum/impulse notes

1. livestream

2. Unit 6 Notes - Rotational Mechanics

3. worked out moments of inertia for hoop, and disk, cylinder, hollow disk, and hollow cylinder

4. rotational inertia of a solid cylinder...see this video for nice explanation!

5. watched video for finding rotational inertia of non-uniform rod

6. found rotational inertia of a washer

7. found rotational inertia of a hollow cylinder (inner radius a and outer radius b)

8. found rotational inertia of a thin rectangular plate

9. Help Video on Rotational Inertia

10. Screencastify introducing the rotational inertia quantity

11. Today's Recording

0. comprehensive momentum/impulse notes

1. livestream

2. Unit 6 Notes - Rotational Mechanics

3. students found the center of mass of a discrete mass distribution, a stick (reference 0 chosen 3/4 of the way along the stick)

4. students found the rotational inertia of a stick about the end and a stick about the middle

5. watched video for finding rotational inertia of a non-uniform disk

6. introduced the parallel axis theorem.

7. discussed how to use parallel axis theorem for following examples: stick about the end from stick about the middle; hoop about an edge from hoop about the middle; sphere about an edge from sphere about the middle; thin plate about the middle from thin plate about an edge

8. showed table of common moments of inertia

9. calculated the rotational energy of a more complicated structure rotating about an end: stick-ball-stick-ball

10. did ranking task calculating rotational inertias of a "t-like" structure comparing I values for various rotational axes

11. defined torque..discussed how to calculate torque, discussed how to assign a direction to torque:

12. great introductory video here on torque

13. discussed all linear/rotational analogies

14. Today's Recording

1. livestream

2. Unit 6 Notes - Rotational Mechanics

3. defined torque..discussed how to calculate torque, discussed how to assign a direction to torque:

4. great introductory video here on torque

5. discussed all linear/rotational analogies

6. worked some torque calculations

7. discussed several rotational dynamics problems

8. worked an example of (review really) for rotational kinematics

9. discussed M problem with mass sliding off frictionless circular hill

10. discussed weekend homework: MC Quizzes on AP Classroom and study Unit 6 material

11. Today's Recording

1. livestream

2. Unit 6 Notes - Rotational Mechanics

3. great introductory video here on torque

4. worked another example (review really) for rotational kinematics

5. discussed a situation in which a cord is wrapped around the rim of a wheel of known rotational inertia I...found the angular acceleration...had to use the relationships torque=(inertia)(alpha) and torque=(magnitude lever arm)(magnitude force)(sin of angle between lever arm direction and force direction). Also discussed how rotational kinematics stuff could then be determined once alpha is found.

6. revisited Atwood's Machine but acknowledged that the pulley has mass. This means that the tension on one side must be greater than the tension on the other side in order to cause the pulley to rotationally accelerate. We had to do force diagrams for both masses (as before), net torque=(inertia)(alpha), and a=R(alpha) to solve for everything. The pulley in this case was a hoop.

7. repeated Atwood's Machine with a pulley that was a disk. Also, just used variables to determine the same quantities found in 6.

8. worked a problem in which a "stone" (really a hanging mass) was released below a stationary pulley and accelerated downward. We found the linear acceleration, the tension, and the mass of the "stone". We were initially given linear motion information about the descent of the "stone". The concepts used were: CA motion analysis, torque=(I)(alpha), a=R(alpha), and Fnet=ma.

9. discussed M problem with mass sliding off frictionless circular hill

10. discussed rolling without slipping (notes here) ... these are separate notes from the unit notes

11. here is a movie explaining how an object rotates and translates at the same time

12. here is another movie relating rolling without slipping

13. Today's Recording

1. livestream

2. Unit 6 Notes - Rotational Mechanics

3. reviewed the derivation of v(t) for an object falling in air with |R|=bv

4. discussed solutions to M13

5. discussed rolling without slipping (notes here) ... these are separate notes from the unit notes

6. used the concept of rolling without slipping (along with conservation of energy) to determine the speed of different rolling shapes at the bottom of a ramp having been released from rest...found v_bot for hollow sphere, hoop, cylinder, and solid sphere.

7. used the concept of rolling without slipping (along with torques, forces, accelerations, and angular accelerations) to determine the speed of a solid sphere at the bottom of a ramp having been released from rest.

8. Today's Recording

1. livestream

2. Unit 6 Notes - Rotational Mechanics

3. discussed a problem in which a marble is allowed to roll down a ramp into a loop de loop....found minimum height for ball to stay on track at top of loop.

4. discussed angular momentum (for point masses and for extended masses)

5. discussed the angular momentum of a point mass traveling at constant speed around a circular path...used L=Iw and also L=r x p

6. discussed the angular momentum of an object moving in a straight line relative to a point not on the line

7. discussed several examples involving calculations of angular momentum

8. discussed the conservation of angular (rotational) momentum

9. discussed an example where angular momentum was conserved

10. Today's Recording

1. livestream

2. Unit 6 Notes - Rotational Mechanics

3. discussed three more examples where angular momentum was conserved (made it halfway through 3rd example)

4. viewed (through 25:22) MIT Lecture Video 20: Topics - Angular momentum is defined relative to an origin whose position can be freely chosen. Angular momentum is therefore not an intrinsic property of a moving object, it depends on the position of the origin. The angular momentum of a projectile's motion is explored. The angular momentum changes along its trajectory. The angular momentum of the Earth's orbit if measured relative to the sun's position, is constant (it is NOT constant if it is measured relative to any other origin) ... Torque equals the time derivative of the angular momentum. The torque acting on the Earth is zero if we choose the sun as our origin. It is NOT zero relative to any other origin. Thus the orbital angular momentum of the Earth (sun as origin) is constant. ... The angular momentum of a disk rotating about its center of mass is proportional to its moment of inertia. The angular momentum associated with rotational motion of a rigid body about a stationary axis through the center of mass is called spin angular momentum. Spin angular momentum is an intrinsic property of a spinning object. It is independent of the point of origin chosen. The Earth spins about an axis through its center of mass. The total angular momentum of the Earth with the sun as the origin is the vectorial sum of the spin angular momentum and the orbital angular momentum.

5. Today's Recording

1. livestream

2. Unit 6 Notes - Rotational Mechanics

3. finished last example where angular momentum was conserved

4. found time it took for a spherical shell to roll down a ramp a known distance using energy...then using torques/forces

5. revisited an Atwood's Machine problem w/ numbers

6. discussed a very intriguing problem with a stationary rotating spherical "pulley" and a stationary rotating cylindrical pulley

7. discussed everything about a conical pendulum (looking at it from a rotational dynamics perspective)

8. introduced the concept of static equilibrium

9. worked multiple examples of static equilibrium

10. Today's Recording

1. livestream

2. Unit 6 Notes - Rotational Mechanics

3. discussed everything about a conical pendulum (looking at it from a rotational dynamics perspective)

4. introduced the concept of static equilibrium

5. worked multiple examples of static equilibrium

6. discussed Unit 4 MC questions

7. Today's Recording

1. livestream

2. Unit 6 Notes - Rotational Mechanics

3. worked one more example of static equilibrium

4. discussed solutions to M16-M20

5. Today's Recording

1. livestream

2. Unit 6 Notes - Rotational Mechanics

3. discussed Unit 4 MC questions

4. discussed solutions to M21-M23

5. students worked practice problems from a review book (both MC and FR)

6. Today's Recording

1. livestream

2. Unit 6 Notes - Rotational Mechanics

3. students took Mechanics Exam 5