PHY 1401 – General Physics I

Rotational Motion

 

Leader: ___________________                      Recorder: __________________________

Skeptic: ___________________                     Encourager: ________________________

 

Materials

Ruler

String

Introductory Rotational Motion Apparatus (Pasco ME-9341)

Stop Watch

Masking Tape

Clay

 

Introduction

      In this experiment we will investigate several aspects of rotational motion including angular velocity, angular acceleration, and torque.  For parts II – V we will use an apparatus consisting of a turntable rotating on a low friction bearing.

 

Part I  Angular Measure

      We are all probably familiar with the concept that there are 360° in a circle.  This forms the basis of how we measure an angle.  If we place an angle with its vertex at the center of a circle, it will cut out a fraction of the circle.  For instance the 30° angle shown in figure 1 cuts out 1/12 of the circle.  Thus any angle that cuts out 1/12 of a circle will have a measure of 1/12 * 360° = 30°. 

 

Figure 1

30° = 1/12 * 360°

 
 

 

 

 

 

 


      Is there anything special about saying there are 360° in a circle?  The answer is that the circle was divided into 360° by the ancient Babylonians 4400 years ago and it stuck.  The Babylonians noticed that the sun took about 360 days to go around Earth and thus divided a circle into 360°.  Other systems are possible.  For example, the military used to use a system in which a circle was divided into 400 gradients or 400 grad. 

 

Q1.  If an angle cuts out 1/12 of a circle, what would be its measure in gradients?

 

 

Q2.  What would be the measure of a right angle in gradients?

 

 

      A system of measure that mathematicians and physicists find very useful is radian measure.  A simple way to think about radian measure is that instead of 360° in a circle, there are 2p radians.

 

Q3.  If an angle cuts out 1/12 of a circle, what would be its measure in radians? (Leave your answer in terms of p.)

 

 

One of the main reasons that mathematicians and physicists find radian measure useful is that when measured in radians there is a very simple relationship for determining angle. 

Notice that if you place an angle at the center of a circle, then it cuts out an arc along the circle.  The length of the arc is denoted by s.  The angle in radians can then be determined from the formula , and this result is very useful in math and physics.

 

 

 

 

 

 

 

 

 


Q4.  For the following four circles, determine the Indicated Angle in two ways.

i)  Multiply the fraction of a circle the angle cuts out by 2p.

ii)  Measure the radius and arc length and use the information to determine the angle.

iii)  Compare your two estimates of the measure of the angle.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 


Part II  Angular Velocity

      If an object is rotating, then its angle is changing with time.  In that case we say that the object has an angular velocity.  Angular velocity is defined as  (1).  The apparatus we are using consists of a horizontal turntable rotating on a low friction bearing.  Once you start the apparatus turning it will remain turning at a fairly constant rate.

 

Q5.  Given a piece of tape and a stopwatch, describe a procedure for determining the angular velocity of the turntable as it spins.

 

 

 

 

Q6.  Your answer for Q5 may have been to time one rotation of the turntable.  What sources of error might occur with that procedure and how could you lessen the source of those errors.

 

 

 

Q7.  Based on your answer to Q6 write a modified procedure for determining the angular velocity of the turntable which will make the errors you identified smaller.

 

 

 

Q8.  Employ the procedure and measure the angular velocity of the turntable when you spin it at three different speeds.    Record the angle in radians.  Organize your data into a data table and be sure to include units.

 

 

 

 

 

 

 

Part III Torque

      In this part we will examine the conditions necessary to produce an angular acceleration.  With the turntable initially at rest, use your index finger to apply a force along the tangent at the edge of the turntable.

 

Q9.  Describe the resulting motion of the turntable.

 

 

      Trying to keep the force about the same, apply the force along the tangent but at four successively smaller radii.  Each time start the wheel from rest.

 

Q10.  Describe how the resulting motion of the turntable changes as you reduce the radius.  In particular describe the affect on the angular acceleration.

 

 

      Starting the turntable at rest each time, compare the effect of increasing the force applied along the edge of the turntable.

 

Q11.  Describe how the angular acceleration changes when you increase the tangential force along the edge of the turntable.

 

 

      Now apply a force along a line directed towards the center of the turntable, i.e. radially.

 

Q12.  Does directing the force radially produce the same angular acceleration as directing it tangentially?  Explain.

 

 

      The quantity that produces an angular acceleration is called torque.  In questions Q10 – Q12 we have investigated three things which affect torque. 

 

Q13.  From your observations, describe how torque depends on the magnitude of the applied force.

 

 

Q14.  From your observations, describe how torque depends on the radius at which the force is applied.

 

 

Q15.  From your observations, describe how torque depends on the direction at which the force is applied.

 

 

      We usually combine these observations into a single formula for torque given by

Torque = Force x Lever Arm, where force is the tangential force that is applied and the lever arm is the distance from the axis of rotation at which the force is applied.  A little more rigorously, torque is defined as t = rF sinq where t is the torque, F is the magnitude of the applied force, r is the radius at which the force is applied and q is the angle between the radius and the force.

 

Q16.  If a force is applied tangentially to a circle what is q?  What is sin q?

 

Q17.  If a force is applied radially to a circle what is q?  What is sin q?

 

Q18.  Torque is maximum for a given force when the angle is _____?

 

Part IV  Angular Acceleration

      When the angular velocity of an object changes the object has an angular acceleration.  In this part of the lab, we will let the apparatus rotate freely, then slow it for a while using a light pressure due to our finger and then let it rotate freely again.  Angular acceleration is defined as   (2)

 

Q19.  During which part of the described motion does the turntable turn at a constant angular velocity?

 

 

Q20.  During which part of the described motion is there an angular acceleration?

 

 

Q21.  The definition of angular acceleration above includes Δω.  How can you determine Δω for the described motion?

 

 

Q22.  The definition of angular acceleration includes Δt.  What is the appropriate Δt to use?

 

Q23.  Describe a procedure for determining the angular acceleration for this procedure using the same materials as in part II.

 

 

 

 

Q24.  Start the turntable spinning and then slow it with a light pressure from your finger.  Record your data in a table and your determination of the angular acceleration in the space below.

 

 

 

 

 

Part V Moment of Inertia

In this part we will examine how mass affects rotational motion

 

Spin the turntable so that it is rotating around 1/2 turn per second.  Take a large ball of clay and drop it as close to the center of the turntable as you can.

 

Q25.  Describe the effect, if any, on the rotation of the turntable.

 

Repeat but drop the clay further from the axis this time.

 

Q26.  Describe the effect, if any, on the rotation of the turntable.

 

Repeat two more times dropping the clay further from the axis, with the last drop being about at the edge of the turntable.

 

Q27.  Describe the effect, if any, on the rotation of the turntable.

 

 

Q28.  Did the effect depend on the distance the clay was dropped from the axis of rotation?  If so, how?

 

 

Again spin the turntable at about 1/2 rotation per second and drop clay balls of increasing mass along the edge of the turntable.

 

Q29.  Describe the effect, if any, on the rotation of the turntable.

 

 

Q30.  Did the effect depend on the amount of clay that you dropped?  If so, how?

 

 

Q31.  Summarize your observations:

Dropping the clay ball further from the axis produced a ____________ change in the rotation.  Dropping larger clay balls at the edge produced a __________ change in the rotation.