1 June 2015 - 6 June 2015. Physical Pendulum.

Purpose

1. to derive expressions for the period of various physical pendulums.
2. to verify the predicted periods by experiment.

Apparatus:

• A set up just like in the picture. This set up is intended for us to hang an object that we want to calculate the period experimentally.

• A thin solid ring with a hollow space in the middle (steel), just like the picture above.
• A chainsaw to cut things up.
• A very thick Styrofoam.

Procedure

1. We are basically going to create several objects, which we will calculate the theoretical period, and compare it to the experimental period.
2. The lists of object's period that we are going to calculate is:
• a solid ring, mass M, with outer radius R and inner radius r
• an isosceles triangle, base B, height H, oscillating about its apex.
• an isosceles triangle, base B, height H, oscillating about the midpoint of its base.
• a semicircular plate of radius R, oscillating about the midpoint of its base.
• a semicircular plate of radius R, oscillating about a point on its edge, directly above the midpoint of the base.
3. We do have the solid ring already, but for the rest, we need to cut it up from the Styrofoam using chainsaw.

4. Measure the weight, the length and the width of every objects.

5. We assemble the set up.
6. Then, we hang the objects as listed in number 2.

7. Record the Period.
8. Compare it to the theoretical period.

Data Analysis:

Measurement data recorded

Solid Ring	Isosceles Triangle	Semicircular Plate
Inner radius r = 0.1390 m	Base = 0.1931 m	Radius = 0.0983 m
Outer radius R = 0.1154 m	Height = 0.1508 m
Weight = 0.3968 kg

solid ring

•  we calculate the Inertia and find the center of mass.

• we calculate the theoretical period by applying torque equals inertia times alpha

•  we did the experiment, and find the period

isosceles triangle, base B, height H, oscillating about its apex

•  we calculate the Inertia and find the center of mass.

• we calculate the theoretical period by applying torque equals inertia times alpha

•  we did the experiment, and find the period

T = 0.7843 s

isosceles triangle, base B, height H, oscillating about the midpoint of its base

•  we calculate the Inertia and find the center of mass.

• we calculate the theoretical period by applying torque equals inertia times alpha

•  we did the experiment, and find the period

T = 0.6789 s

semicircular plate of radius R, oscillating about the midpoint of its base

•  we calculate the Inertia and find the center of mass.

• we calculate the theoretical period by applying torque equals inertia times alpha

•  we did the experiment, and find the period

T = 0.6838 s

semicircular plate of radius R, oscillating about a point on its edge, directly above the midpoint of the base

•  we calculate the Inertia and find the center of mass.

• we calculate the theoretical period by applying torque equals inertia times alpha

•  we did the experiment, and find the period

T = 0.6683 s

PERCENT ERROR

Object	Theoretical T (s)	Exp. T (s)	Percent Error
Solid Ring	0.7175	0.718088	0.08%
isosceles triangle, oscillating about its apex	0.783	0.7843	0.17%
isosceles triangle, oscillating about the midpoint of its base	0.6995	0.6789	-2.94%
semicircular plate of radius R, oscillating about the midpoint of its base	0.683	0.6838	0.12%
semicircular plate of radius R, oscillating about a point on its edge, directly above the midpoint of the base	0.67	0.6683	-0.25%

Average percent error = 0.71 %

Conclusions

• We manage to find the period of several objects, such as the solid ring, an isosceles triangle, and semicircular plate, using the equation of torque and simple harmonic motion in small angle.
• The average percent error is 0.71% , which is very good.
• Some error in this lab probably come from the fact that we use theta instead of sin theta because the value is very similar (but not the same), when the displacement of theta is really small.
• We might also push the pendulum to hard, such that the displacement is no longer considered small, and will affect the error in calculation even more.

THANK YOU PROFESSOR WOLF FOR AN AWESOME SEMESTER!