Physics Laboratory I. Dinamics Rotational Inertia. Ins. Fatma Nur AKI

Transcription

1 Physics Laboratory I Dinamics Rotational Inertia Ins. Fatma Nur AKI fnaki@ticaret.edu.tr

2 Vernier Calipers There are special devices for taking measurements. For example Vernier calipers are used to meausere small widths and diameter while a travelling microscope is used to measure small lengths.

3 How Does a Vernier Caliper Work? To use a venier calliper close the jaws lightly over the object to be measured and if measuring something with a round cross section ensure the axis of the object is perpendicular to the calliper. Use the bottom scale which is in metric units ignoring the top. The tick mark found on the left on the sliding scale will allow you to read from the fixed scale the number of whole millimetres when the jaws are opened and check to see that one of the tick marks aligns with a tick mark on the fixed scale. The number of aligned tick marks on the sliding scale will tell you the number of tenths of millimetres.

4 Using Vernier 4

5 Vernier 5

6 Experiment : Rotational Inertia of Disk and Ring / Conservation of Angular Momentum EQUIPMENT REQUIRED - Balance - Rotational Inertia Accessory (ME-8953) - Rotating Platform (ME-8951) - Smart Pulley Photogate Disk, Ring Ruler

7 Purpose A non-rotating ring is dropped onto a rotating disk and the final angular speed of the system is compared with the value predicted using conservation of angular momentum.

8 Theory F = 0 = 0 Inertia: Newton's first law of motion states that "An object at rest stays at rest and an object in motion stays in motion with the same speed and in the same direction unless acted upon by an unbalanced force." Objects tend to «keep on doing what they're doing». Inertia: the resistance an object has to a change in its state of motion.

9 Rotational Inertia (Moment of Inertia): The moment of inertia of an object depends on where the axis of rotation is. The moment of inertia can be found by breaking up the object into little pieces, multiplying the mass of each little piece by the square of the distance it is from the axis of rotation, and adding all these products up:

10 Moment of inertia is the mass property of a rigid body that defines the torque needed for a desired change in angular velocity ( )about an axis of rotation. Moment of inertia depends on the shape of the body and may be different around different axes of rotation.

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13 Some Video links

14 Theory The rotational inertia of a disk about its center of mass is given by: where M is the mass of the disk and R is the radius of the disk.

15 Theory Theoretically, the rotational inertia, I, of a ring about its center of mass is given by: where M is the mass of the ring, R1 is the inner radius of the ring, and R2 is the outer radius of the ring.

16 the final rotational inertia of the combined disk and ring is I f = (1/2)M 1 R 2 + (1/2)M 2 (r 12 +r 22 )

17 When the ring is dropped onto the rotating disk, there is no net torque on the system since the torque on the ring is equal and opposite to the torque on the disk. Therefore, there is no change in angular momentum. Angular momentum is conserved. where Ii is the initial rotational inertia and i is the initial angular speed.

18 Procedure 1-) Using a ruler, measure the diameter of the disc, and calculate radius of disc by dia/2 and save to Table 1. Diameter= 2R Radius= R

19 2-) By using vernier (or ruler) measure the inner and outher diameter of ring. Calculate the radius of ring by dia/2 and write the table 1.

20 3-) Measure the mass of ring and disc.

21 SETUP Setup Level the apparatus using the square mass on the track

22 Assemble the Rotational Inertia Accessory as shown in Figure 7.1. The side of the disk with the indentation for the ring should be up. Mount the Smart Pulley photogate on the black rod on the base and position it so it straddles the holes in the pulley on the center rotating shaft. Run the Smart Pulley Timer program

23 Analysis Calculate the expected (theoretical) value for the final angular velocity and record this value in Table 1. Calculate the percent difference between the experimental and the theoretical values of the final angular velocity and record in Table 1.

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