Physical Pendulum
Samuel
Ellis
Mia
11-28-2016
Purpose:
Derived expressions for the period of various physical pendulum. Verify your predicted period by experiment.
Theory:
Procedure:
1. derive expressions for the moment of inertia of the ring about this point and the period of this ring behaving as a physical pendulum2. Make physical measurement of the relevant quantity for the ring
3. Measure the actual period of the ring, acting as a physical pendulum
4. compare your experimental result with your theoretical result
5. Cut our or find objects of the appropriate shapes. Measure the appropriate dimensions of each one, and their respective masses
6. Attach a thin piece of making tape to the bottom of each object
7. Use the same setup as above to measure the small-amplitude period of oscillation for each one.
8. Compare the actual and theoretical values for the periods using the actual measured dimensions for the various object.
Measured Data:
Ring_inner = 20.59 cm
Ring_outer = 21.8 cm
Height_1 = 12 cm
Based_1 = 13 cm
Height_2 = 13 cm
Based_2 = 13.4 cm
Ring_outer = 21.8 cm
Height_1 = 12 cm
Based_1 = 13 cm
Height_2 = 13 cm
Based_2 = 13.4 cm
Graph:
(Above, is the oscillating ring graph. The period slowly decreasing due to frictional force acting between rod and and the ring.)
(Above, is upright triangle graph. This graph has lesser decreased because we used paper clip instead of metal ring. So the frictional force is lesser.)
(Above, is upside down triangle. The period is faster than the upright triangle. Because it has less mass on the bottom)
Calculation:
I_pt = I_cm + m*r^2
= m*r^2 + m*r^2
= 2*m*r^2
I = I*๐ฐ
m*g*sin๐*r = 2*m*r^2*๐ฐ
๐ฐ = g/2*r * sin๐
w^2 = g/(2*r)
w = sqrt(g/(2*r))
Based on above equation, I got 0.928 for my calculated period for the ring.
Conclusion:
In this experiment, we derived a equation to determined the period of oscillating ring and compared it with actual period of the ring. As usual, we have made some assumption. First, the angle we pushed can not be larger than 10 degree. Because if it is less than 10 degree, the amount of error is so small, we can just ignore it. Secondly, we assumed there's no frictional force acting between two materials. And lastly, we assumed the rod for holding the object is parallel to the surface.