PASCO ME-8950A COMPLETE ROTATIONAL SYSTEM - Manual (Page 13)

012-05293F Complete Rotational System
9
EQUIPMENT NEEDED
- Rotating Platform (ME-8951) - Rubber band
- Projectile Launcher (ME-6800) - White paper and carbon paper
- Projectile Collision Accessory (ME-6815) - Thread
- Photogate/Pulley System (ME-6838) - Meter Stick (SE-6895)
- DataStudio Software - Mass and Hanger Set (ME-8967)
- PASCO Interface (see Note) - Calipers (SF-8711)
Purpose
The muzzle velocity of the Projectile Launcher can be determined by shooting the ball into the catcher
mounted on the platform and conserving angular momentum during the collision. This result can be
checked by finding the muzzle velocity of the Launcher by shooting the ball horizontally off the table.
Theory
A ball is launched horizontally and embeds in the catcher mounted on the platform. The platform then
rotates. See Figure 1.1.
Angular momentum is conserved during the collision but energy is not conserved. The angular
momentum before the collision is equal to the angular momentum after the collision:
where m
b
is the mass of the ball, v
o
is the muzzle velocity of the ball, R is the distance between the ball
and the axis of rotation, I is the rotational inertia of the catcher, ball, and rotating platform after the
collision, and
ω is the angular velocity of the system immediately after the collision.
Solving for the muzzle velocity of the ball gives:
L m
b
v
0
R I ω = =
0
10
1
2
3
4
5
6
7
8
9
20
11
12
13
14
15
16
17
18
19
21
22
24
10
9
8
7
6
5
4
3
2
1
20
19
18
17
16
15
14
13
12
11
24
23
22
21
0
10
1
2
3
4
5
6
7
8
9
20
11
12
13
14
15
16
17
18
19
21
22
24
10
9
8
7
6
5
4
3
2
1
20
19
18
17
16
15
14
13
12
11
24
23
22
21
R
Rotating
Platform
"A" base
w
Projectile
Launcher
Projectile Collision Accessory
("catcher")
Experiment 1: Conservation of Angular Momentum
(Projectile Version)
v
o
Figure 1.1 Conservation of Angular Momentum
Note: If you are
using a PASPORT
interface, you will
also need a Digital
Adapter (PS-2159)