A particle of mass m is moving along a trajectory given by x=x₀+a cos ω₁ t and y=y₀+b sin ω₂ t. The torque acting on the particle about the origin at t=0 is

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(3) +m y₀a ω₁²̂k. Torque needs the position and the force, both at t=0. Position at t=0: x=x₀+a cos 0=x₀+a and y=y₀+b sin 0=y₀. Differentiate twice: x=-aω₁² cos ω₁ t and y=-bω₂² sin ω₂ t. At t=0: x=-aω₁² and y=0, because sin 0=0. So ⃗F=m(-aω₁², 0) — it points purely along -x at that instant. In the plane, τ_z=xF_y-yFₓ. τ_z=(x₀+a)(0)-(y₀)(-m aω₁²)=+m y₀a ω₁². τ⃗=+m y₀a ω₁²̂k.

A particle of mass m is moving along a trajectory given by x=x₀+a cos ω₁ t and y=y₀+b sin ω₂ t. The torque acting on the particle about the origin at t=0 is

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