How Is Angular Velocity Calculated in This Classical Mechanics Scenario?

[vrinda mukund]

Homework Statement

A particle has a velocity u = -V0 i + V0 j and position (d,0) at t=0. At any time t its position in polar coordinates is (r,theta) and velocity V = V0 cos theta i + (V0-V0sin theta) j. At t =t, angular velocity of the particle at the origin will be -----------------

Homework Equations

angular velocity w = d(theta)/dt

The Attempt at a Solution

actually i didnt understand the question itself. why these two velocities are given.

 

[Astronuc]

The particle is moving in two dimensions.

There is v_x = dx/dt and v_y = dy/dt. Now if one writes x = r cos θ, and y = r sin θ, then try dx/dt and dy/dt, what is the result?

Also think about ω = dθ/dt, and θ = ωt + θ_o.

Is ω costant? Is u constant?

 

[vrinda mukund]

i feel that U is a constant as no variables appear in the expression for u. nothing is mentioned about w in the question. the answer should be v0(cos theta)/r.
the radial velocity of the patricle about the origin should be -V0(1-sin theta)