- #1

EddiePhys

- 131

- 6

## Homework Statement

Find the

**total tension**acting on a rod rotating about its end with an angular velocity of w as a function of its length x(length)

## Homework Equations

F = ma[/B]

## The Attempt at a Solution

Let the function be T(x) where x is the length of the rod.

Considering an interval between x and x + dx

For an increment in dx, let the function change by dT(x)

dT(x) = T(x+dx) - T(x)

T(x+dx) is the tension acting on a rod of length x + dx

T(x) is the tension acting on a rod of length x

Therefore, dT(x) is the tension acting on the tiny element of length dx

dT(x) = dm(w^2) x

dm = ρdx

∫dT(x) = ρ(w^2)∫ xdx from T(x) = 0 at x = 0 to T(x) at x = x.

This gives me tension as a function of the length of the rod

Is what I've done correct & rigorous? Is my general approach to calculus alright or am I viewing things wrong?