Solve Torsional Pendulum Homework Statement

• Bryon
In summary, a uniform meter stick is hung from a thin wire and is twisted to oscillate with a period of 5 seconds. After sawing off the stick to a length of 0.76 meters and rebalancing it, the stick now oscillates with a period of 3.8 seconds. The torsional constant is calculated using the moment of inertia and the period equation, and the final period is found using the ratio of the original and final lengths. This method simplifies the calculation process.
Bryon

Homework Statement

https://wug-s.physics.uiuc.edu/cgi/courses/shell/common/showme.pl?cc/DuPage/phys2111/fall/homework/Ch-15-SHM/torsion-pendulum/4.gif

A uniform meter stick is hung at its center from a thin wire. It is twisted and oscillates with a period of 5 s. The meter stick is then sawed off to a length of 0.76 m, rebalanced at its center, and set into oscillation.

With what period does it now oscillate?

L = 1m
L(final) = 0.76m
T = 5s

Homework Equations

Moment of Inertia: I = (1/12)*M*L^2
period: T = 2pi*sqrt(I/K) Where K is the torsional constant

The Attempt at a Solution

I first found the torsional constant:

K = [(1/12)*M*(1^2)]/[(T/(2pi))^2] = 0.13459M

So no I have K = 0.13459M

T(final) = 2pi*[sqrt((1/12)*M*(0.76^2)/0.13159M)] = 3.8s

The answer looks correct but I'm not sure, any ideas? Thanks!

Last edited by a moderator:
instead of going for so much calculation...
u could have done it like this...

becauz..

T=2*pi*(I/K)^0.5

and u have I=(M*L^2)/12

so jus take the ratio

T1/T2=L1/L2

where T2 is the time period when the length is 0.76

Oh yeah it does...cool.

1. What is a torsional pendulum?

A torsional pendulum is a type of simple harmonic oscillator that consists of a mass connected to a rod or wire that is suspended from a fixed point. The mass is allowed to rotate about its axis, creating a twisting motion.

2. How do you solve a torsional pendulum homework statement?

To solve a torsional pendulum homework statement, you will need to use the equation T = 2π√(I/k), where T is the period of the pendulum, I is the moment of inertia, and k is the torsion constant. You will also need to use the equation τ = -kθ, where τ is the torque, k is the torsion constant, and θ is the angle of rotation.

3. What factors affect the period of a torsional pendulum?

The period of a torsional pendulum is affected by the moment of inertia, which is determined by the mass and distribution of the mass on the pendulum, as well as the torsion constant, which is determined by the material and geometry of the wire or rod used. The amplitude of the pendulum's motion and the presence of any external forces can also affect the period.

4. How is a torsional pendulum different from a simple pendulum?

A torsional pendulum differs from a simple pendulum in that it has a rotational motion rather than a linear motion. This means that the restoring force is provided by torsion rather than gravity. Additionally, the period of a torsional pendulum is not affected by the amplitude of its motion, unlike a simple pendulum.

5. What are some real-world applications of torsional pendulums?

Torsional pendulums are commonly used in scientific experiments to study the behavior of oscillating systems. They are also used in various instruments, such as mechanical clocks and seismometers. In industry, torsional pendulums are used to test the strength and durability of materials, such as wires and cables.

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