Rigid Pendulum g derivation equation

In summary, the general equation for "g" in terms of measurable quantities is g = [({[(To / Tbar)^(2)][(Mbar / 12)(L^2 + b^2)] + Mh^2}*4pi^2) / (T^2)] / (Mh). This was derived by rearranging equations (1) to (4) and substituting them into each other to eliminate variables. The final equation is based on the concept of a rigid pendulum and can be found in a lab report provided in the link.
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Rigid Pendulum "g" derivation equation

Homework Statement



Determine the general equation for "g" in terms of measurable quantities(M, Mbar, h, L, b, T, To, Tbar) from the following equations: (refer below)


Homework Equations



(1) T = 2pi(I / Mgh)^(0.5)

(2) (Io / Ibar) = (To / Tbar)^(2)

(3) Ibar = (Mbar / 12)(L^2 + b^2)

(4) I = Io + Mh^2



The Attempt at a Solution



- Alright first i re - arranged eqn. (1) so that g = [ (I*4pi^2) / (T^2)] / (Mh)

- Then i re - arranged eqn. (2) so that Io = [(To / Tbar)^(2)](Ibar)

- I then used eqn (3) and subbed it into the new equation (2)

Io = [(To / Tbar)^(2)][(Mbar / 12)(L^2 + b^2)] (5)

- I then subbed in our newly formed eqn (5) into eqn (4)

I = [(To / Tbar)^(2)][(Mbar / 12)(L^2 + b^2)] + Mh^2 (6)

- Now i sub eqn (6) back into our re arranged equation for g

g = [({[(To / Tbar)^(2)][(Mbar / 12)(L^2 + b^2)] + Mh^2}*4pi^2) / (T^2)] / (Mh)

and that's my final answer
 
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What is a Rigid Pendulum?

A Rigid Pendulum is a physical system consisting of a rigid body attached to a fixed point by a hinge or pivot. It is used to study the motion of a pendulum under the influence of gravity.

What is the derivation equation for a Rigid Pendulum's acceleration due to gravity?

The derivation equation for a Rigid Pendulum's acceleration due to gravity is given by g = (4π²L)/T², where g is the acceleration due to gravity, L is the length of the pendulum, and T is the period of the pendulum's oscillation.

What factors affect the acceleration due to gravity in a Rigid Pendulum?

The acceleration due to gravity in a Rigid Pendulum is affected by the length of the pendulum, the mass of the rigid body, and the angle at which the pendulum is released. It is also influenced by external factors such as air resistance and the Earth's rotation.

How is the Rigid Pendulum's period of oscillation related to the acceleration due to gravity?

The period of oscillation for a Rigid Pendulum is inversely proportional to the square root of the acceleration due to gravity. This means that as the acceleration due to gravity increases, the period of oscillation decreases.

What are the real-world applications of the Rigid Pendulum?

The Rigid Pendulum is commonly used in physics education to demonstrate the principles of pendulum motion and gravity. It also has practical applications in timekeeping, such as in the design of pendulum clocks. In addition, it is used in seismology to measure the Earth's gravitational field and in geology to study the Earth's interior structure.

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