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## Homework Statement

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A particle of mass m slides (both sideways and radially) on a smooth frictionless horizontal table. It is attached to a cord that is being pulled downwards at a prescribed constant speed v by a force

**T**(

**T**may be varying)

Use

**F**=m

**a**in polar coordinates to derive an expression for the tension

**T**(

**T**will depend on r and θ and how they may be changing)

Show the particle's polar coordinates satisfy r

^{2}dθ/dt = constant

HINT: The only horizontal force on the particle is T and it acts purely in the inward radial direction. Also, dr/dt is known and it is equal to -v

## Homework Equations

**a**= (r''(t)w

^{2})r_hat +(r(t)θ''(t) + 2r'(t)θ'(t))θ_hat

L(t) = L_o ????

## The Attempt at a Solution

Not entirely sure how to get started. I've identified that a_r must be zero (since dr/dt is a constant, r''(t) must be zero making a_r zero). I've also set up the equation a_θ = r(t)θ''(t) - 2vw since r'(t) = v and θ'(t) = w. The issue I'm having is trying to identify another equation for the acceleration (or force) in the θ direction, and then from there rectifying that into T.