# Torsional Pendulumn- Inertia and Period

• lc99
In summary, when the balance wheel of a torsional pendulum is doubled in size and the torsional constant remains the same, with the density of the disk remaining the same but both the radius and thickness doubling, the period of the pendulum goes up by a factor of sqrt(8). This is because the moment of inertia increases by a factor of 8, causing the period to increase by sqrt(8). The options given do not include this factor, and it was initially thought that the period would decrease due to a mistake in calculating the moment of inertia. However, if the thickness doubles, the mass will double, and if the radius doubles, the mass will also double.
lc99

## Homework Statement

Assume the balance wheel of a torisonal pendulumn is doubled in size but the torison constant of the spring remains the same. The density of the disk remains the same, but bot the radius and the thickness double. What happens to the period of the pendulumn?

a) Period doubles
b) period goes up by a factor of sqrt(2)
c) period goes up by factor of four
d) period goes up by factor of 4sqrt(2)
e) none of the other answers

## Homework Equations

omega = sqrt(k/I)
k= torsional constant
I = 1/2MR^2
R is doubled and M is doubled (since thickness/size doubled)

## The Attempt at a Solution

My answer is e) none of the answers because i calculated that the period actually goes down...
w = sqrt(k/I)
I = 1/2MR^2 = 1/2 (2M)(2R)^2 = 8 (1/2MR^2)

--> w = sqrt(k/(8*I)) = 1/ sqrt(8) * sqrt(k/I)
W = 2pi/T --> T = 2pi / (sqrtk/I)
--> 1/sqrt(8) T
the period went down by sqrt(8).

Do I read correctly that you think that omega AND T both go down by the same factor ?

BvU said:
Do I read correctly that you think that omega AND T both go down by the same factor ?
Oh man. I found my mistake! The period went up by sqrt(8). Omega went down by sqrt(8) . But, squrt(8) isn't any of the options? I must have calculated the moment of inertia incorrectly?

M doubles ?

lc99 said:
Oh man. I made a mistake! The period went up by sqrt(8). Omega went down by sqrt(8) . But, squrt(8) isn't any of the options?
BvU said:
M doubles ?
BvU said:
M doubles ?
i thought so because the size/thickeness doubles

If the thickness doubles, the mass doubles.
If the radius doubles, the mass ...

lc99

## What is a torsional pendulum?

A torsional pendulum is a simple device used to study the effects of torsional (twisting) forces on an object. It consists of a mass suspended from a wire or rod, which can rotate freely about its axis.

## How does inertia affect the motion of a torsional pendulum?

Inertia is the resistance of an object to changes in its motion. In a torsional pendulum, the inertia of the suspended mass determines its resistance to twisting. The greater the inertia, the longer it takes for the pendulum to complete one full oscillation.

## What is the period of a torsional pendulum?

The period of a torsional pendulum is the time it takes for the pendulum to complete one full oscillation, or one full cycle. It is affected by the length of the pendulum, the mass of the suspended object, and the force of gravity.

## How does the length of the pendulum affect its period?

The period of a torsional pendulum is directly proportional to the length of the pendulum. This means that the longer the pendulum, the longer it takes to complete one full oscillation. This relationship is known as the "law of isochronism."

## How can the period of a torsional pendulum be measured?

The period of a torsional pendulum can be measured by counting the number of oscillations it completes in a certain amount of time and then calculating the average period. It can also be measured using a stopwatch or a motion detector, which can track the pendulum's motion and calculate its period.

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