- #1

Smouk

- 7

- 1

## Homework Statement

There's a pendulum with mass m and longitude L strapped to a disk with radius R that rotates with an angular velocity ω. Calculate the angle that the pendulum is shifted (Φ) depending on ω.

You are given m, L, R, ω, g. Calculate Φ depending on ω.

Little drawing (with my amazing Windows Paint skills):

## Homework Equations

Centripetal Force = mω^2r //Will call it CF from now on

Gravitational Force = mg //Will call it GF from now on

The tension is the resultant from both gravitational (opposite direction) and centripetal forces.

## The Attempt at a Solution

Using what we've seen on the 2nd point.

CF = sin(Φ) * L

sin(Φ) = CF/L

Φ = arcsin(mω^2r/L)

Now we have Φ depending on ω but we still have to know what is r exactly so we proceed:

d = sin(Φ) * L

R, r and d form a right triangle so we apply Pythagora´s theorem:

r = sqrt(R^2 + d^2) = sqrt(R^2 + sin^2(Φ) * L^2)

That way we end up with:

Φ = arcsin(mω^2*sqrt(R^2+sin^2(Φ) * L^2) / L)

After doing some calculations you end up with:

sin^2(Φ) - sin^2(Φ) = (mRω^2/L)^2

Which basiclly is:

0 = (mRω^2/L)^2

I just think I'm not understanding this problem or I'm doing something wrong somewhere, I'm not asking for anyone to solve it but just to tell me what I'm doing wrong so I can figure it out.

Thanks to everyone!