Physics 1 lab: 8 Conservation of Angular Momentum PDF

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Summary

Post Lab write up of laboratory experiment Conservation of Angular Momentum...

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Conservation of Angular Momentum

Professor Brian Schwartz Ulugbek Ganiev, Hamood, Mohdhar 4/7/16

Objective: This experiment illustrated the conservation of angular momentum using air-mounted disks to measure the angular acceleration. The initial angular momentum is compared to the final angular momentum and the same process is repeated with the rotational kinetic energy, which is not conserved for inelastic collisions. Theory/Procedure: We will be experimenting with translational as well as rotational movement and trying to represent their relationships using certain equations as well as known variables like R (radius). Conservation of angular momentum states that in absence of external torque, angular momentum ( L = I ω), of a system is conserved. The angular velocity in radians/second can be calculated using the formua (ω = 2 πn/200). The moment of inertia I of a circular disk of mass M and radius R with axis through its center can be calculated using the formula (I = MR²/2). To find velocity for a ball that will be dropped from a ramp onto the disk we use the formula ( v =d √ g/2 h ¿

Part 1: We inserted the valve pins so that the two disks of the apparatus were free to rotate independently; this ensured that the two disks rotated at different speeds, then we removed the pin from the upper disk so that the two disks rotated together, having undergone an inelastic collision. Measured the diameter of the disks and using the masses printed on the apparatus we calculated the moments of inertia of the rotating disks. Measured the angular velocity of each disk before the collision, and that of the combination after the collision. Repeated this procedure four times, as detailed below. 1. Start with the lower disk with ω = 0, and the upper disk in motion. 2. Start with the upper disk with ω = 0, and the lower disk in motion. 3. Have both disks in motion rotating in the same direction. 4. Have the two disks rotating in opposite directions.

Mass, kg (m)

Diameter, m

Radius, m

Moment of Inertia, kg* m2

Upper Lower

1.3541 1.3416

Trial

0.125 0.125

0.0625 0.125

(I) 0.00264 0.00262

Reading of

Angular velocity,

Angular Momentum, kg *

%

counter, n

rad/s

m2/s (L)

diff

Before

After Before

Afte

Before

After

.

r 1

U 34

L 0

173

U 10.

L 0

5.43

U 0.02

L 0

Total 0.029 0.029 0

2

7 0

25

125

9 0

7.9

3.93

9 0

0.02

0.021 0.021 0

3

36

2 43

390

2 11.5 13.

12.3

0.03

1 0.03

0.056 0.065 0

4

5 39

0 44

24

12.

5 13.

0.75

0 0.03

5 0.03

0.004 0.004 0

4

4

4

9

7

7

Trial

Rotational kinetic energy, J (E )

% diff.

U

Before L

After Total

1

0.157

0

0.157

0.078

1.01

2

0

0.0822

0.082

0.041

1

3

0.175

0.239

0.414

0.399

0.04

4

0.203

0.253

0.456

0.001

3.03

5

Questions:

1. Why is angular momentum conserved in these collisions (Part I and II)? Note that linear momentum is not conserved in Part II. How then is angular momentum conserved? a. Angular momentum is conserved because equal and opposite torque applies, for the same time. In part I the angular momentum was transferred from one disk to another as they collided. This could be observed when one disk was stationary it began to rotate when colliding with a moving disk. Thus momentum was not created nor destroyed. Part II was similar to part I in that there also was conservation of angular momentum. This was observable again when the ball hit the stationary disk and the disk began to move. The momentum of the ball was transferred to the disks. 2. Derive Equation 9

3. Is kinetic energy conserved in part II?

a. Kinetic energy is not conserved in part II of the experiment as it is an inelastic collision and the initial kinetic energy is converted into some other type of energy. Conclusion: The purposed of this lab was to appreciate the conservation of angular momentum. We observed and recorded the initial momentum of inertia as well as the final and therefore could compare the difference to find if it truly was conserved. The angular momentum of a rigid object is defined as the product of the moment of inertia and the angular velocity. This is analogous to linear momentum, which we have discussed previously in lab and lecture, and is subject to the fundamental constraints of the conservation of angular momentum principle if there is no external torque on the object....