20-May-2017: Lab 16: Angular acceleration

Lab 16: Angular acceleration

Author: Weisheng Zhang

Lab Partners: Tian Cih Jiao, Kitarou, Nina Song, Joel Cook, Eric Chong

Date: May 10th & 15th, 2017

Purpose of the lab:
The purpose of the lab is to measure the angular acceleration when a known torque is applied to a rotatable object. After figuring out the angular acceleration, we use the collected data to find moment of inertia in these cases.

Theory/Introduction:

Part 1:

For the first part, we use control the changing to get the result of this lab.

For EXPT 1, 2, 3, we change the mass of hanging mass.

Then for 1 and 4, we compare the change of radius which can change the torque.

Then 4, 5, 6 are for figure out the effect of changing the rotating mass.

Part 2:

For the convenience of calculation, we let counterclockwise direction be positive and the other way be negative.

A counterclockwise torque caused by the tension in the string is speeding up the hanging mass to descend, while the clockwise friction torque is slowing down the mass. Therefore,

Torque of string - Torque of friction = MoI (Moment of Inertia) of disk * angular acceleration down

After the hanging mass reaches its possible lowest point, both of the torques start act in the clockwise direction, thus slowing down the disk.

-torque of string - torque of friction = MoI of disk * angular acceleration up

Then what we need to do is calculating data.

Summary of apparatus/experimental procedure:
Pasco rotational sensor, Macbook Pro with LoggerPro, Lab Pro Kit, disks of different materials, torque pulleys, hanging mass and hose clamp are used for this lab.
Set up the apparatus. Due to the poor timing resolution of the sensors, we can not take advantage of the default angular acceleration vs. time graph. Instead, we need to use the graphs of angular velocity to measure the angular acceleration as the mass moves down and up. Hose clamp is used to control the number of disks on operation. It is open for one disk operation and closed for two disk operation. We can turn on the compressed air so that the disks can rotate separately. It is important to make sure that the disk can rotate independently when needed.

Measured data:
Mass of the top steel disk = 1357 grams
Diameter of the top steel disk = 126.1 millimeters
Mass of the bottom steel disk = 1348 grams
Diameter of the bottom steel disk = 126.1 millimeters
Mass of the top aluminum disk = 466 grams
Diameter of the top aluminum disk = 126.1 millimeters
Mass of the smaller torque pulley = 9.99 grams
Diameter of the smaller torque pulley = 24.6 millimeters
Mass of the larger torque pulley = 36.59 grams
Diameter of the larger torque pulley = 49.7 millimeters
Mass of the hanging mass supplied with the apparatus = 24.62 grams

Here are the graphs from LoggerPro:
EXPT 1 (hanging mass only, small torque pulley, top steel disk)

 EXPT 2 (2 * hanging mass, small torque pulley, top steel disk)

 EXPT 3 (3 * hanging mass, small torque pulley, top steel disk)

 EXPT 4 (hanging mass only, large torque pulley, top steel disk)

 EXPT 5 (hanging mass only, top aluminum torque pulley, top aluminum disk)

 EXPT 6 (hanging mass only, large torque pulley, top steel + bottom steel disk)

Analysis:
This is the calculation from one of our member.

Conclusion:
Angular acceleration increases when torque increases, radius increases or MoI decreases. This conclusion is made through comparison experimental sets mentioned in previous parts.