Find Tension of the rotating rod at a distance x

[Tanya Sharma]

Homework Statement

A homogeneous rod with a length L and a mass M rotates with an angular velocity ω in a horizontal plane around an axis passing through its end.Find the tension of the rod at a distance x from its axis of rotation .

Homework Equations

The Attempt at a Solution

$$T(x)-T(x+dx)=\frac{M}{L}ω^2xdx$$
$$-dT=\frac{M}{L}ω^2xdx$$
$$\int_{T(0)}^{T(x)}dT=-\int_{0}^{x}\frac{M}{L}ω^2xdx$$
$$T(x)-T(0)=-\left[\frac{M}{2L}ω^2x^2\right]_{0}^{x}$$

Now when x=L,T(L)=0

Thus,$T(0)=\frac{M}{2L}ω^2L^2$

Hence, $T(x)=\frac{M}{2L}ω^2(L^2-x^2)$

Kindly check the work if mathematically the steps are correct...

 

[ehild]

It looks good.

ehild

 

[Tanya Sharma]

ehild...Thank you very much