Lab 20: Physical Pendulum

Physics Lab #20 started on 6/3/15
Physical Pendulums
Annemarie Branks
Professor Wolf

Objective: Determine the periods of two physical pendulums swinging at two different orientations each.

Procedure:
     1.  Cut out an isosceles triangle and a semicircle out of a stiff material. Measure their dimensions.

     2.  To determine their theoretical periods, T, first find their centers of mass. 

     3.  Determine the moments of inertia for each shape with the pivot at opposite ends. You will need to use the Parallel axis Theorem to do this.

     4.  Using Torque=Inertia*angular acceleration, find omega. Use omega to find the period for each shape at their different orientations.

     5.  Set up the experiment so that each shape can swing from two different points. To do this, tape small metal circles on each side and run a paper clip through it. Have the paper clip securely attached to a metal rod. We used clay to do this. Connect a photogate to logger pro and orient it so the shape will swing through it.

     6.  Run the experiment under the Pendulum Timer file and get their periods.

• For the semicircle swinging from the flat edge the Period is 0.651110 seconds. Reminder that the calculated period was 0.662 seconds.
• For the semicircle swinging from the point on the curve, the Period is 0.660176 seconds. Reminder that the calculated period was 0.649 seconds
• For the triangle swinging from its tip, the Period is 0.699378 seconds. Reminder that the calculated period was 0.686 seconds
• For the triangle swinging from its edge, the Period is 0.700107 seconds. reminder that the calculated period was 0.860 seconds.

The calculated and the actual periods are all relatively within the same ball park, except from the last trial which was more off than the others. These differences could be attributed to sources of error

Sources of Error/Uncertainty:

• The photogate/LoggerPro gave varying periods for each swing and we used the last period it detected rather than the average
• An uncertainty of +/- 0.1 cm when measuring the shapes
• The shapes were not perfectly cut with precision.
• The way the paperclip was bent changed the way the shape swung
• The circles we taped onto the shapes could have slightly changed the center of mass
• Its possible there was a slight draft in the room that caused the shapes to swing undesirably

Lab 19: Solid Ring Pendulum

Physics Lab #19 started on 6/1/15
Solid Ring Pendulum
Annemarie Branks
Professor Wolf

Objective: Determine the period of a pendulum ring.

Procedure:
     1.  Measure the inner and outer diameters of the ring with the vernier caliper. No need to weigh the ring because the masses will cancel out. For our little diameter, we measured 115.1 mm, and for the big diameter we measured 139.0 mm.

      2.  Notice the indent on the ring. The indent was made at the average of the two radii. This is where the ring will be swung on the rod. Using the moment of Inertia for a ring  about its center of mass, we can use the parallel axis theorem to find the moment of Inertia about the pivot. The moment of Inertia at the pivot was 0.00811 meters^2 * Mass of the ring. The calculations are shown below:

     3.  Using Torque=Inertia*angular acceleration, plug in your found Inertia and solve for angular acceleration. The constant in front of the sine theta is omega squared. Find your omega value. For us, it was 8.77 rad/s as seen in the above photo.

     4.  Now that omega has been found, the period can be found and ours turned out to be 0.717 seconds.

     5.  With the theoretical value found, set up the ring to swing at its indent on the rod. Place a photogate underneath it. A piece of paper or tape could be used if the ring does not pass through the photogate easily. With the photogate set up to LoggerPro, find the period. The period we go from LoggerPro was 0.719909 seconds which is pretty close to our theoretical value. We suspect there are sources of error since LoggerPro gave some variation of the period, but it always stayed around 0.72 seconds.