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**1. Homework Statement**

A particle moves with const speed v along the curve r(θ) = a(1+cos θ).

Starting with the general expression for the velocity vector

**v**in polar coordinates solve for θ_dot in terms of v, k, and θ. What does the sign of θ_dot signify?

**2. Homework Equations**

**v**= r_dot*r_hat + r*θ_dot*θ_hat

**v**= v * v_hat

r(θ) = a(1+cos θ)

r_hat = x_hat cos Θ + y_hat sin θ

v

**3. The Attempt at a Solution**

r_dot = -a sin θ

solving for θ_dot:

θ_dot = (

**v**- r_dot * r_hat)/(r*Θ_hat)

I am lost here, I think I am missing some important relation and something that comes out of the fact that the speed in constant but I don't know what.

Any help would be greatly appreciated thanks.

Edit:

I think I've got it, since the magnitude of unit vectors are one and θ_dot is a scalar I can just stop at

θ_dot = (

**v**- r_dot * r_hat)/(r*Θ_hat)

= (v*v_hat - r_dot * r_hat)/(r*Θ_hat)

= (v-r_dot)/r

= (v+a sin θ)/(a + a cos θ)

Is this right? What does the sign mean then, just the value?

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