Physics

Physics

Problem

A particle of mass 2 kg2 \text{ kg} is moving such that at time tt, its position, in meter, is given by r⃗(t)=5i^−2t2j^\vec{r}(t) = 5\hat{i} - 2t^2\hat{j}. The angular momentum of the particle at t=2st = 2\text{s} about the origin in kg m−2s−1\text{kg m}^{-2} \text{s}^{-1} is : a. −80k^-80\hat{k} b. (10i^−16j^)(10\hat{i} - 16\hat{j}) c. −40k^-40\hat{k} d. 40k^40\hat{k}
Intuitive explanation

Angular momentum L⃗=r⃗×mv⃗\vec{L} = \vec{r} \times m\vec{v} captures how a particle's motion "spins" around a point. Here, you need to extract the velocity by differentiating the position function, evaluate both r⃗\vec{r} and v⃗\vec{v} at t=2 st = 2\text{ s}, then compute the cross product with the given mass. The key is remembering that only the perpendicular components of position and velocity contribute to the magnitude of angular momentum.

Intuitive explanation

Angular momentum L⃗=r⃗×mv⃗\vec{L} = \vec{r} \times m\vec{v} captures how a particle's motion "spins" around a point. Here, you need to extract the velocity by differentiating the position function, evaluate both r⃗\vec{r} and v⃗\vec{v} at t=2 st = 2\text{ s}, then compute the cross product with the given mass. The key is remembering that only the perpendicular components of position and velocity contribute to the magnitude of angular momentum.

Browse the problem library