Lab#20: Conservation of Linear and Angular Momentum

Conservation of Linear and Angular Momentum

Samuel
Ellis
Mia
11-21-2016

Purpose:

To understand how conservation of momentum can translate to both linear and angular direction.

Theory: 

When object is rotating, it will have a tangential and linear direction. When the tension is release, the object will move toward tangential direction. And since we know that momentum is conserved, therefore, we can use tangential momentum and change that to angular momentum. In addition, we can use kinematic equation to find how far or how long object travel. Because velocity is the same throughout flying period.  

Procedure:

1. Use the aluminum to disk, and mount the ball-catcher on top of the small torque pulley using a gray-capped thumbscrew.

2. Using the method of Experiment 6, determine the moment of inertia of the disk and ball catcher. Also measure of the ball. 

3. Place the ramp on the edge of a table. Determine the horizontal velocity of the ball as it roll off the end of the ramp

4. Mark a starting point on the ramp

5. Release the ball from this staring point and note where the ball strikes the floor(a floor of carbon paper over a sheet of white paper will leave a mark for measuring)

6. Measure the distance L and h. The horizontal velocity of the ball is then equal to L/t where t = 2*h/g.

7. If you have time, you may want to calibrate the ramp by determining the horizontal velocity for a variety of starting points. If you plan on doing the optional part of the analysis for this experiment, you will also need to record the starting height of the ball. 

8. Roll the ball down the ramp so that it is caught by the ball-catcher. Quickly remove the ramp, so it doesn't disturb the rotational of the ball-catcher, and record the reading of the digital display. Record the horizontal velocity of the ball based on your earlier measurement, and also record the radius.

9. Repeat your measurement.

10. Using procedure outlined above, make the measurement necessary to investigate the relationship between the angular momentum imparted to the system.

Measured Data:

Mass_ball = 28.9 grams

Diameter_ball = 19 mm

h = 95 cm

L = 59.5 cm

d = 16 cm

hang mass = 24.6 g

diameter_pulley = 47.9 mm

w = 2.269 rad/s

r_ball to axis = 7.6 cm

Graph:

(Above, is the graph of ball-catcher rotating on top of disk. The consistent slope is cause by the rotating disk. Since it's angular velocity is the similar, so the slope looks almost identical.)

(Above, is the angular acceleration graph of it going up and down.)

Calculated Data:

Find hanging time in air
Δy = -0.5*g*t^2
0.95 = -4.9*t^2
t = sqrt(0.95/4.9)
t = 0.440

Δx = v*t
0.59*t = v*(0.440)
v = 1.35 m/s

Find w
1.
(0.076)(0.02898)(1.35) = (1.05*10^-3)+0.0289*0.076^2+ 2/5 *0.0289*0.009^2
w = (0.002965/0.001217)
w = 2.43 rad/s

2.
0.042*0.0289*1.35 = 0.00105 + 0.0289*0.042^2 + 2/5 *0.0289 * 0.009^2
w = (0.001638/0.001102)
w = 1.48 rad/s

Conclusion:

In this experiment, we used already prepared equipment to conduct this experiment. We used LoggerPro to calculated the angular velocity of the rotating disk with ball-catcher. We then measured the height, distance and length of the ramp. With all the measured data, we are able to use kinematic equation to find the air time during the fall. And according to conservation of momentum, all energy conserved. So for our calculated data for angular momentum, we got 2.43 and 1.48. And for theoretical we got 2.43 and 1.49. Which is almost identical and it also prove momentum is conserved.