PHYS 1401 – General Physics I

Torque and Angular Acceleration

 

Leader: _________________________          Recorder: __________________________

Skeptic: _________________________         Encourager: ________________________

 

Materials

Laptop

LabPro

Force Probe with loop of string around the clamp hole

Smart Pulley

Introductory Rotational Motion Apparatus with square plate

Ring stand with right angle clamp

Mass hanger and gram mass set

Digital Calipers

 

Introduction

      In this lab we will examine the connection between the torque applied to a rotating object and the angular acceleration that is produced.  Our apparatus will consist of a turntable with an attached string.  The string will be draped over a smart pulley which will measure the acceleration of the string.  A force probe will be suspended from the string and will measure the tension in the string.

 

Procedure

1.  Set up

Clamp the smart pulley with the right angle clamp and adjust the height so that the string travels horizontally over the smart pulley.  Attach the force probe to the loop on the string and position the smart pulley at the edge of the table so that the force probe can drop straight down.  Plug the force probe into CH 1 on the LabPro and plug the smart pulley into DIG/SONIC 1.  Open LoggerPro and open the experiment file “n2lrot” as directed by your instructor.  Make sure that the switch on the force probe is in the 10 N position.

 

2.  Zero the force probe

It is important to zero the force probe correctly before each trial.  With the hook up, hold the force probe by the case – not the hook – and position it so that there is slack in the string.  Zero the force probe by clicking on the 0 button.  Zero the force probe in the same way before each trial.

 

3.  Data Collection

Use the digital calibers to determine the radius of the pulley wheel around which you will wind the string. 

 

Radius = ___________________

 

Roll up the string so that the force probe is just below the photogate.  Click on the collect button.  Once data collection starts, release the force probe. 

Q1) Sketch the appearance of the graphs of velocity vs. time acceleration vs. time and force vs. time in the space below.

 

 

 

 

Click on the window showing the velocity vs. time graph.  Click and drag over the area on the graph where the force probe was falling.  Click on the linear regression button  to fit a line to that part of the data.

 

Q2)  What will the slope of this line tell you?

 

 

Q3)  Record the acceleration for the string.

 

 

Q4)  How is the acceleration of the string related to the tangential acceleration of the pulley wheel the string is wrapped around?  Explain.

 

 

Q5)  Determine the angular acceleration of the turntable from your measured values.

 

 

Q6)  If the turntable had an angular acceleration, was a torque exerted on it?  Explain.

 

 

Q7)  Draw a free body diagram for the turn table.

 

 

Q8)  Which of the forces that you showed in your free body diagram exert a torque on the turntable.  Explain why the other forces don’t exert a torque.

 

 

Click on the force vs. time graph

Q9)  Determine the torque exerted on the turntable.

 

Record the values you determined for the torque and the angular acceleration in the data table shown below in the row for trial 1.

 

Trial

Angular acceleration

Torque

1

 

 

2

 

 

3

 

 

4

 

 

5

 

 

 

Suspend the 50 g mass hanger from the loop of string on the back of the force probe. 

 

P10)  If additional mass is suspended from the force probe. What effect will there be on the tension in the string?

 

 

P11)  What effect will there be on the torque on the turn table?

 

 

P12)  What effect will there be on the angular acceleration of the turn table?

 

 

Roll up the string so the force probe is just below the mass hanger again and measure the torque and angular acceleration in the same manner as before.  Add your data to the data

table.

 

Repeat 3 more times each time adding an additional 50 g of mass to the mass hanger.

 

Q13)  Were your predictions about adding more mass so the force probe correct?  Explain how they were wrong if they were wrong.

 

Use LoggerPro or Excel to construct a properly labeled graph of Torque vs. angular acceleration for the turn table.

 

Q14)  Do your data appear to lie on a line?  Does the line go through the origin?

 

 

Newton’s second law applied to rotational motion states that the torque is proportional to the angular acceleration.  So, ideally your line should go through the origin.  However, there are effects such as friction in the turn table and pulley and mass of the pulley which will probably make your line not go through the origin.  We can model these as additional torques and obtain τ = Iα + τo where τ0 is the offset due to the effects mentioned above.

 

Use the linear regression button in LoggerPro  or add a trendline in excel to the graph

 

Q15)  What does the slope of your line tell you?

 

 

 

Q16)  Determine the moment of inertia of the turn table.

 

 

Lift the top table of the turn table and place the rectangular plate on top of the lower table.  Return the top table.

P17)  If you keep the mass on the force probe the same as your last trial, what effect will there be on the angular acceleration of the turn table?  Explain.

 

 

Measure the torque and angular acceleration as before.  Record your values below.

 

α = _______________

 

τ = _______________

 

Q18)  Was your prediction correct.  Explain how it was wrong if it was wrong.