- #1
quantum13
- 66
- 0
Homework Statement
A regular pendulum is swinging back and forth. Assuming it starts from a horizontal position, find an expression for its tangential velocity.
(I don't know if the question is posed right, I just asked myself it as a challenge)
2. The attempt at a solution
using a freebody diagram, I know that the tangential vector is the tangential component of weight. let Θ be the angle such that the tangential component of weight is mgsinΘ.
F = ma
mgsinΘ = ma
gsinΘ = dv/dt
I know I am supposed to do
v = ∫gsinΘ dt
but I have no clue how to do that except using rotation equations,
Θ = α/2 t^2 + ωt = a/2r t^2 + v/r t = gcosΘ/2r t^2 + v/r t
which leaves me with messy algebra that brings me in circles...
can anyone help me set up this problem?