Kinetic energy of electron in polar coordinates

[texan14]

Homework Statement

An electron's position is given by r(t)=r(0)+c1*t, θ(t)=θ(0)+c2*t, where r(0), c1, θ(0), and c2 are known constants. What is the kinetic energy of the electron? (mass=m)

Homework Equations

KE=(1/2)Iω²=(1/2)mr²ω²

The Attempt at a Solution

plugging in m for mass, r(0)+c1*t for radius, and c2 for ω
(1/2)(m)(r(0)+c1*t)²(c2)²

This isn't the correct answer, so I'm fairly certain I've messed up on my "r" value somehow.

It's supposed to equal (1/2)(m)(c1²+r²c2²)

Where am I going wrong?

 

[tiny-tim]

hi texan14!

An electron's position is given by r(t)=r(0)+c1*t, θ(t)=θ(0)+c2*t, where r(0), c1, θ(0), and c2 are known constants. What is the kinetic energy of the electron? (mass=m)
…
KE=(1/2)Iω²=(1/2)mr²ω²

what on Earth are you doing?

that's for a rigid body with angular velocity ω

this is a spiral … you have no idea what ω(t) is, it certainly isn't θ'

start again, and just use v = (r',rθ') ​

(you do know how to prove that, don't you? … if you don't, then look it up)