PHYS 1401 – General Physics I

Moment of Inertia

Leader: ___________________ Recorder: __________________________

Skeptic: ___________________ Encourager: ________________________

Materials

Torque feeler at instructor’s desk w/ mass hanger and gram mass set

Spring Scale, Green (5 N capacity)

Pasco Rotational Motion Apparatus with rotating platform attached

Stop watch

Introduction

In this lab we will examine two things. First, we will review the idea of torque introduced in the previous lab. Second, we will examine the effect of applying a constant torque

Part I Review of Torque

For this part of the activity there is one set up at the instructor’s desk. Each group should take a turn completing this part of the activity. While waiting for your group’s turn, you can continue this activity beginning at part II below.

In this part of the activity you will use a device called a “torque feeler”. A torque feeler is a handle attached to a rod from which masses can be hung at different distances. You hold the handle with both hands, one on either side of the rod, with palms facing down. In our case the “rod” is actually a meter stick. A mass hanger is hung from a clamp on the meter stick.

Procedure

Move the clamp to the 50 cm mark on the meter stick and hold the torque feeler so that the rod is horizontal. While supporting both ends of the torque feeler, suspend the mass hanger from the clamp and place an additional 150 g on the mass hanger. Support the handle with your closed hands but do not grasp the handle firmly, instead allowing the handle to rotate in your hand. Release the side of the torque feeler opposite the handle and observe the subsequent motion. You can remove the additional mass from the mass hanger.

Q1) Describe the motion of the torque feeler. Did it fall straight down, did it move diagonally, swing on an arc, etc.?

In this case, the weight exerts a force that causes the torque feeler to speed up along an arc of circle. A force applied this way produces a torque.

Q2) Did the angular velocity of the torque feeler change?

Q3) If the answer to Q2) was yes, then the torque feeler had and angular _______.

Now grip the handle firmly and hold the rod horizontally with the mass on the hanger. Now that you are not allowing the handle to rotate so you are also exerting a torque on the torque feeler

Q4) How does the torque you exert compare to the torque exerted by the weight? Explain.

While holding the torque feeler horizontally, add an additional 100 g to the mass hanger.

Q5) Do you feel a change in the torque you have to exert when you add the extra 100 g?

Add another 100 g.

Q6) Do you feel a change in the torque you have to exert when you add the extra 100 g?

Add another 100 g

Q7) Do you feel a change in the torque you have to exert when you add the extra 100 g?

Q8) As the force applied by the weight goes up, how does the torque change (bigger, smaller, no change)?

Replace the mass hanger with the 500 g mass on the hook. Feel the torque you have to apply to hold the torque feeler horizontal. Now move the clamp so that it is 10 cm from the handle. Again, hold the torque feeler horizontally.

Q9) Is the torque you have to exert as big as when the mass hanger is 10 cm form the handle as when it was in the middle of the rod?

While holding the torque feeler horizontally, move the clamp holding the 500 g mass out in 10 cm increments. Stop after each increment to feel the torque. Continue until the clamp reaches the end of the stick.

Q10) As the weight is moved away from the handle, how does the torque change? (bigger, smaller, stays the same)

Up to this point we have investigated how the torque depends on the force creating it and how it depends on the distance from the handle that it is exerted. There is one more factor that affects torque.

Start with the rod held horizontally and with the 500 g mass hanging from near the end of the rod. Slowly rotate your wrists back so you raise the end of the torque feeler. Continue until the torque feeler is almost vertical.

Q11) As you rotate the end of the torque feeler up, how does the torque that you have to apply change?

When you hold the rod horizontally, the angle between the rod and the weight is 90°. When the rod is almost vertical, the angle between the rod and the weight is about 0°.

Q12) The torque is maximum when the angle is _____, and the torque is minimum when the angle is _______.

Summary Questions for Part I

S13) As the weight of the hanging mass increases, what effect was there on the torque exerted by the weight.

S14) As the distance the mass was located from the handle increased, what effect was there on the torque exerted by the weight?

S15) As the angle between the meter stick and the weight decreased, what effect was there on the torque?

Part II – Moment of Inertia

In this part of the lab we will investigate rotational inertia. For motion in a line, inertia is determined by the mass. We will investigate the factors that affect the resistance to change in rotational motion.

Procedure

The rotating platform has masses that can be slid. Loosen the wing nuts and slide both masses so that they sit next to each other with their inner edges sitting on the 0 cm mark.

Wind up the string around the largest of the three wheels below the rotating platform. Hook the spring scale on the loop at the end of the string. Hold the platform and pull on the spring scale so that it reads 2 N. Release the platform and pull on the string so that you maintain a constant force of 2 N. You may need to practice this several times. Once you can pull with a fairly steady force of 2 N, then starting from rest, use the stopwatch to time 3 complete revolutions of the apparatus pulling the entire time with a constant 2 N force.

Q16) Record the time.

Q17) If the force is constant, then what will be true about the applied torque in this case?

Q18) What is the initial angular velocity for this situation?

Q19) What is the angular displacement?

Q20) Assuming that it is constant, determine the angular acceleration for this situation. show your work in the space below.

Now loosen the wing nuts and move each mass so that its inner edge now sits at the 10 cm mark on the rotating platform. Tighten the wing nuts again.

Q21) Did you change the amount of mass on the platform?

Q22) If you wind the string around the same wheel and apply a 2 N force again will the torque change from your first trial? Explain.

P23) Predict if the angular acceleration will be the same, less or greater if you conduct the same procedure as before.

Repeat the same procedure as before.

Q24) Record the time for this trial.

Q25) Determine the angular acceleration for this trial.

Now loosen the wing nuts and move each mass so that its inner edge now sits at the 20 cm mark on the rotating platform. Tighten the wing nuts again.

Q26) Did you change the amount of mass on the platform?

Q27) If you wind the string around the same wheel and apply a 2 N force again will the torque change from your first two trials? Explain.

P28) Predict if the angular acceleration will be the same, less or greater if you conduct the same procedure as in the previous trial.

Repeat the same procedure as before.

Q29) Record the time for this trial.

Q30) Determine the angular acceleration for this trial.

Q30) Did the amount of mass on the platform change in this experiment?

Q31) As the distance from the axis that the mass was located increased, what happened to the angular acceleration.

Q32) Not only mass affects rotational inertia, but also where it is located. What effect is there on the resistance to changes in rotational motion by placing the mass further from the axis? Cite specific evidence from this experiment to support your answer.