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The Air Top and The Omega Machine

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Prerequisites

Lab Activities

The students study the precession of a top which is subjected to an external torque with the objective of demonstrating the validity of the relationship T = dl/dt where T is the external torque on a rigid body whose angular momentum is L. Specifically, they test to see that:

a. for a fixed torque, the frequency of precession varies as 1/w where w is the angular frequency with which the top is spinning;

b. the product of the precessional frequency and the angular frequency is proportional to the external torque; and

c. for a fixed torque, the product of the precessional frequency and the angular frequency is independent of the angle of the top with respect to the vertical.



Omega Machine

The students study the motion of a golf ball projectile in a reference frame rotating at a constant speed. Specifically, the experiment is intended to verify that in a frame rotating at angular frequency, w, there is a pseudoforce acting on a body of mass m given by

F = -mw x (w x r') - 2m(w x v')

where the primes denote variables in the rotating reference frame.

The Omega Machine consists of a circular rotating platform on which a rectangular grid is painted. Attached to the platform and suspended approximately eight feet above it is a Polaroid camera which can be remotely activated. A golf ball gun, which can be fired at any angle or elevation with respect to the surface of the platform, is also attached to the side of the rotating platform. Using strobe illumination, the students take a photograph of the path of the golf ball with respect to rotating grid. After determining the positions of the golf ball wrt the the grid and the initial conditions of position and velocity, they write a computer program which will integrate the equation of motion for the ball (given in the writeup) thereby modeling the system. The object is to try to produce computer simulated orbits which are as close to the experimental case as possible.

Course Level

Introductory: P15

Student Handouts

Equipment

Number of set-ups available: 1

Air Top Station:

1 air pump/variac
1 air top (stand and ball)
1 strobe light/stand
1 balance
1 stop watch
1 ball parameter sheet
1 box of misc. tops and things
1 box of weights and disks

The Omega Machine Station:

1 air pump/variac
1 air top (stand and ball)
1 strobe light/stand
1 balance
1 stop watch
1 ball parameter sheet
1 box of misc. tops and things
1 box of weights and disks

Air Top

Air Top Apparatus


Omega Machine

Omega Machine Apparatus

Notes


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Site contact: largent@Dartmouth.EDU

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