Weight and Axle II, 1Q20.10

Topic and Concept:

• Rotational Dynamics, 1Q20. Rotational Energy

Location:

• Floor Item: ME, South Wall

Abstract:

Two equal masses are mounted on a radial bar fixed to a horizontal axle with a pulley. A weight is released which causes it to spin. The masses can be moved in and out. The rotational speed and acceleration of the spinning axle can be monitored with a Pasco photogate.

Important Setup Notes:

• If using the PASCO interface is desired for the graphical output, a 24-hour notice is required.

• The axle spends fast and there is No emergency breaking system on the axle to stop it from rotating.

• To stop the axle's quickly, use your flat hand and place it on the horizontal axle like a brake until it stops. Watch out for the the peg on the axle for the weight.

Setup and Procedure:

1. Select a radial position for the two weights (this sets the moment of inertia for the axle). This is done by loosening their respective set screws, shifting their position, and re-tightening the screws. A pliers will be needed.
2. Select which weight to use in accelerating the axle and connect it to the rope with the snap clip to it's eye-hook.
3. Suspend the weight from the axle by placing the slip ring over the peg on the axle.
4. Wind up the rope connected around the axle by rotating the axle in the clockwise direction until the weight is almost touching the axle.
5. Slide the "stop bar" located on the right-hand-side forward so that the bars holding the axle weight in place. This will keep the axle from rotating until you're ready.
6. When ready, slide the "stop bar" back to its original position to let the weight drop and thereby accelerate the rotation of the axle. Once the weight drops off the axle, the rotational speed of the axle will remain constant (approximately...blame friction).
7. One can also just hold the axle with one had hand without using the stop bar if desired. This method works best if using the Paso Interface Computer.

Optional Addition of the PASCO Interface with Computer:

1. Lock the computer cart in place, plug in the power supply, and start the computer.

2. Please refer to the PASCO Interface Computer, A1.EQ.100 page for general operations of the computer.

3. Before booting up the computer, Place the Weight and Axle II cart nearby and plug in the Pasco photogate to the Pasco interface. ie. Make sure that the Photo-gate 1/4" plug is in Slot "A" of the PASCO Interface box.

4. Open the experimental setup file which is located on the desk top in the folder PASCO Interface under the file name Weight-Axle-1Q20.10.ds
5. The display from the computer can be routed to a projector, if desired.
6. When ready record the data, click on "Start" at about the same time as when you release the Weight.

7. If the auto stop feature is setup within Data Studio, the program will automatically stop recoding after the set time interval that was setup. If not, then just click "Stop" in Data Studio after the weight leaves the axle. (see plot below for an example or PASCO Interface Computer, A1.EQ.100 page).

8. Note that the Gate-wheel, shown in the photos below, for the photogate has a Spoke Arc Length of 0.015m and a spoke Angle Spacing of 36 degrees.

Cautions, Warnings, or Safety Concerns:

• The sliding weights on the radial arm can slide off and break the rotating arm if the weight locking screws are not tight enough.
• The rotating arm spends "very" fast and can hit you, if you get too close.
• The falling weight make a good noise when the cord is released from the axle.
• The Cord from the hanging weight wipes around with it is released from the axle.

Discussion:

Any rotating object has rotational kinetic energy given by;

KE_rot = (1/2)*I*ω²

Where I is the moment of inertia of the object and ω is the angular speed. The axle has an adjustable moment of inertia. This can be changed by shifting the radial positions of the brass weights. The further away from the axis of rotation these weights are, the larger I will become for the axle. ω is determined, in our case, by the weight that drops from the axle. This is because the rate of angular acceleration is determined by the applied torque being given by;

α = τ_net / I = m*g*R_axle / I

Thus, the greater the mass of the weight, the faster our final angular speed will be. This can be investigated in a more quantitative manner by using the PASCO Interface Computer along with the photogate that is mounted on the rear of the alxe. The template provided in Data Studio plots angular displacement versus time as well as angular speed versus time. The slope of each plot gives ω(t) and α(t) respectively. Knowing R_axle, the mass of the weight used, the acceleration of gravity, and α, we can extract I and thereby calculate the rotational energy of our system.