Weight and Axel II, 1Q20.10

Topic and Concept:

• Rotational Dynamics, [:RotationalDynamics#RotationalEnergy: 1Q20. Rotational Energy]

Location:

• [:MechanicsCabinet#MEFloorItems: Floor Item: ME, South Wall]

attachment:WeightAxleII03-400.jpg

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:

• N/A

Setup and Procedure:

1. If use of Pasco photogate is desired (skip to step 6 otherwise), lock the computer cart in place, plug in the power supply, and start the computer.
2. Place the Weight and Axel II cart nearby, and plug in the Pasco photogate to the Pasco interface.
3. The display from the computer can be routed to a projector, if desired.
4. Double click the icon labeled "Data Studio". A template should exist for this demo in {insert file path here}.
5. When you are ready to perform the demo later, click "Acquire Data" {is this right??} to begin sampling.
6. 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.
7. Select which weight to use in accelerating the axle and connect it to the rope with the snap clip.
8. Suspend the weight from the axle by placing the slip ring over the peg on the axle.
9. Wind up the rope connected around the axle by rotating the axle in one direction until the weight is almost touching the axle.
10. Slide the "stop bar" in front of the bars holding the weights. This will keep the axle from rotating until you're ready.
11. 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).

Cautions, Warnings, or Safety Concerns:

• Don't drop the weights on your foot...ouch =(

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 photogate. 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.

Videos:

• [https://www.youtube.com/user/LectureDemostrations/videos?view=1 Lecture Demonstration's Youtube Channel]

References:

• [https://en.wikipedia.org/wiki/Rotational_energy Wikipedia - Rotational Energy]

• [https://en.wikipedia.org/wiki/Torque Wikipedia - Torque]

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