PHY 2425 – Engineering Physics I

Introduction to Rotational Motion

Leader: ___________________ Recorder: __________________________

Skeptic: ___________________ Encourager: ________________________

Materials

Part I

Ruler, String

Part II-III

Introductory Rotational Motion Apparatus (Pasco ME-9341), Stop Watch, Masking Tape

Part IV

Introductory Rotational Motion Apparatus (Pasco ME-9341)

Part V

Introductory Rotational Motion Apparatus (Pasco ME-9341), 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

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.

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 Angular Acceleration

When the angular velocity of an object changes, then 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

Q9. During which part of the motion will there be an angular acceleration?

Q10. Describe a procedure for determining the angular acceleration for this procedure using the same materials as in part II.

Q11. Start the turntable spinning and then slowly 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 IV 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.

Q12. 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.

Q13. 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.

Q14. 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.

Q15. 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 Q13 – Q15 we have investigated three things which affect torque.

Q16. From your observations, describe how torque depends on the magnitude of the applied force.

Q17. From your observations, describe how torque depends on the radius at which the force is applied.

Q18. 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.

Q19. If a force is applied tangentially to a circle what is q? What is sinq?

Q20. If a force is applied radially to a circle what is q? What is sinq?

Q21. Torque is maximum for a given force when the angle is _____?

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.

Q22. Describe the effect on the rotation of the turntable.

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

Q23. Describe the effect 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.

Q24. Describe the effect on the rotation of the turntable.

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

Q25. Describe the effect on the rotation of the turntable.

Q26. 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.