Period of a Physical Pendulum: Finding T for a Uniform Disk

In summary, the conversation discusses finding the period, T, for small oscillations of a uniform metal disk with a mass of 9.81 kg and radius of 8.99 m, oscillating as a physical pendulum about an axis through the edge. The equations used were I = (1/2)MR^2 for a disk with axis through the center of mass and I = (3/2)MR^2, after using the Parallel Axis Theorem, for a disk with axis through the edge. The final result obtained was T = 3.2 seconds, although it was incorrect and the individual was seeking assistance in finding the error. The suggestion was made to carry out the process symbolically before plugging in
  • #1
yaylee
22
0

Homework Statement


A uniform metal disk (M = 9.81 kg, R = 8.99 m) is free to oscillate as a physical pendulum about an axis through the edge. Find T, the period for small oscillations.


Homework Equations



I (uniform disk, with axis through center of mass) = (1/2)MR^2
T = 2π√(I/mgd), where d = distance from center of mass to point of rotation (axis)
I (uniform disk, with axis through the edge = (3/2)MR^2, after using Parallel Axis Theorem:
I (center of mass) + Md^2, where d = RADIUS of the disk:

The Attempt at a Solution


Plugging in for T, we have 2π√(I/(9.81)(9.81)(8.99).
After plugging in I = (3/2)*(9.88)*(8.99)^2, we can plug and chug away:

T = 3.2 seconds, however, this was incorrect.

I was wondering where I went wrong here, thanks again !
 
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  • #2
You might find that fewer "finger" errors can creep in if you carry out more of the process symbolically before plugging in numbers.

Put your expression for the moment of inertia into the expression for the period and simplify before going numerical :wink:
 

FAQ: Period of a Physical Pendulum: Finding T for a Uniform Disk

1. What is a physical pendulum?

A physical pendulum is a rigid body that is free to rotate about a fixed axis. It consists of a mass attached to a pivot point, which allows for oscillatory motion.

2. How is the period of a physical pendulum calculated?

The period of a physical pendulum is calculated using the equation T = 2π√(I/mgd), where T is the period, I is the moment of inertia of the pendulum, m is the mass of the pendulum, g is the acceleration due to gravity, and d is the distance from the pivot point to the center of mass.

3. How does the length of a physical pendulum affect its period?

The period of a physical pendulum is directly proportional to the square root of its length. This means that as the length of the pendulum increases, its period also increases.

4. What factors can affect the period of a physical pendulum?

The period of a physical pendulum can be affected by various factors such as the length of the pendulum, the mass of the pendulum, the amplitude of its swing, and the strength of gravity.

5. Why is the period of a physical pendulum important?

The period of a physical pendulum is important because it can be used to measure the strength of gravity, as well as the moment of inertia of an object. It also has practical applications in fields such as engineering and physics.

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