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Pendulum (mathematics) - Wikipedia

Contents · 1 Simple gravity pendulum · 2 Small-angle approximation. 2.1 Rule of thumb for pendulum length · 3 Arbitrary-amplitude period · 4 Approximate formulae ...

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Why does the formula for kinetic energy have a half in it? - Quora

Newton's second law says that force equals mass times acceleration, [math]F = ma[/math]. ... What will the value of kinetic energy of moving body of mass m and its speed is ... Consider the work done as an object moves from momentum zero to MV due ... Why is the equation for kinetic energy 1/2mv^2 when the equation for ...

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Units and Dimensions - Dimensional Analysis, Formula, Applications

Units and dimensions - Understand Dimensional analysis with Limitations and Applications. Know Dimensional Formulas of Quantities and Quantities with Same ... Dimensional analysis is the practice of checking relations between physical ... For example, I can compare kinetic energy with potential energy and say they ...

For more information, see Units and Dimensions - Dimensional Analysis, Formula, Applications

According to the Principle of Homogeneity, the dimensions of each term of a dimensional equation on both sides should be the same. This theory allows us to convert the units from one form to another.

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https://byjus.com/physics/dimensional-analysis/#:~:text=Principle%20of%20Homogeneity%20states%20that,from%20one%20form%20to%20another.

Given that

\frac{1}{2} mv^2 = mgh

Step 1: Set up a dimensional formula for kinetic energy

K.E = \frac{1}{2} mv^2   where, m - mass and v -  velocity

Dimensional formula [math] = [M] [L^2 T^{-2}] [/math]

[math]=\ [ML^2T^{-2}][/math] ....................(1)

Step 1: Set up a dimensional formula for potential energy

P.E = mgh , where m - mass, g - acceleration due to gravity ( 9.8 m/s^2 ).

Dimensional formula [math] = [M] [LT^{-2}] [L] [/math]

[math] = [M L^2 T^{-2}] [/math] ...................(2)

From equation (1) and (2)

\frac{1}{2} mv^2 = mgh

[math] [M L^2 T^{-2}] = [M L^2 T^{-2}] [/math]

L.H.S = R.H.S

Since the dimensions of the LHS and RHS are the same, the equation is dimensionally correct.