Calculating Density and R of a Compound Pendulum: A Step-by-Step Guide

You correctly calculated the density and R for the given equilateral triangle suspended from one of its corners. You also correctly used the formula for calculating density. In summary, you correctly computed the density and R for an equilateral triangle suspended from one of its corners.
  • #1
Akibarika
9
0
Little help in compound pendulum

Homework Statement


there is an equilateral triangle T with sides of length B. Suspend this triangle from a pivot throught on of its corners, so that it is free to swing about this corner in the plane of the tringle.

I want to ask how to compute the density p(x,y) and the R whcih from the pivot point to the center of gravity of the triangle.

In fact I found the soluation, but I don't know it is right or not.
Could anyone check it with me?

Homework Equations


p(x,y)=m/A


The Attempt at a Solution


A=sqrt(3)/4 * B^2
therefore p(x,y)=(4*sqrt(3)*m)/(3*B^2)

about the R:
GRAPH.jpg

cos 30 = sqrt(3)/2
R = (B/2)*(2/sqrt(3)) = (sqrt(3)*B)/3

did I make any mistake??

Thanks a lot
 
Last edited:
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  • #2
You did not.
 

1. What is the purpose of calculating density and R of a compound pendulum?

The purpose of calculating density and R of a compound pendulum is to determine the mass per unit volume and the radius of gyration of the pendulum. This information can be used to understand the physical properties of the pendulum and its behavior when in motion.

2. What equipment is needed to calculate the density and R of a compound pendulum?

The equipment needed includes a compound pendulum, a ruler or measuring tape, a stopwatch or timer, and a scale or balance that can measure in grams. A protractor may also be helpful for measuring angles.

3. How do you calculate the density of a compound pendulum?

To calculate the density of a compound pendulum, you will need to measure its mass and volume. First, measure the mass of the pendulum using a scale or balance. Then, measure the length of the pendulum using a ruler or measuring tape. Finally, use the formula density = mass/volume to calculate the density of the pendulum.

4. How do you calculate the radius of gyration of a compound pendulum?

The radius of gyration of a compound pendulum can be calculated using the formula R = √(I/m), where R is the radius of gyration, I is the moment of inertia, and m is the mass of the pendulum. The moment of inertia can be calculated by multiplying the mass of the pendulum by the square of its distance from the pivot point.

5. What are some potential sources of error when calculating density and R of a compound pendulum?

Potential sources of error when calculating density and R of a compound pendulum include measurement errors, variations in the density of the material, and air resistance. It is important to ensure accurate and precise measurements and to repeat the experiment multiple times to account for any discrepancies.

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