The position vector of a particle of mass m is $\vec{r}$ (t) = αt³î + βt²ĵ, where α = (10/3) m·s⁻³, β = 5 m·s⁻² and m = 0.1 kg. At t = 1 s, which statement(s) is/are true?
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Question

The position vector of a particle of mass m is r ⃗ \vec{r} r (t) = αt³î + βt²ĵ, where α = (10/3) m·s⁻³, β = 5 m·s⁻² and m = 0.1 kg. At t = 1 s, which statement(s) is/are true?

G1 Physics · Accepted Answer

Start from Newton’s laws for translation and rotation: ΣF=Ma and Στ=Iα. Use the geometrical constraint/energy relation stated in the question and solve for the required quantity. The result is A: The velocity is v⃗ = (10î + 10ĵ) m·s⁻¹.; B: The angular momentum about the origin is L⃗ = -(5/3)k̂ N·m·s.; D: The torque about the origin is τ⃗ = -(20/3)k̂ N·m..