The time dependence of the position of a particle of mass m = 2 is given by r → t = 2 t i ^ - 3 t 2 j ^ . Its angular momentum, with respect to the origin, at time t = 2 is:

r → = 2 t i ^ - 3 t 2 j ^ v → = 2 i ^ - 6 t j ^ Momentum p → = m v → = 4 i ^ - 12 t j ^ ∴ angular momentum L → = r → × p → = 2 t i ^ - 3 t 2 j ^ × 4 i ^ - 12 t j ^ = - 24 t 2 k ^ + 12 t 2 k ^ = - 12 t 2 k ^ At time t = 2 L → = - 48 k ^

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Physics - Rotation Question with Solution | TestHub

PhysicsRotationAngular momentumMedium2 minPYQ_2019

PhysicsMediumsingle choice

The time dependence of the position of a particle of mass $m = 2$ is given by $\vec{r} (t) = 2 t \hat{i} - 3 t^{2} \hat{j}$ . Its angular momentum, with respect to the origin, at time $t = 2$ is:

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Answer:

Solution:

$\vec{r} = 2 t \hat{i} - 3 t^{2} \hat{j}$
$\vec{v} = 2 \hat{i} - 6 t \hat{j}$
Momentum $\vec{p} = m \vec{v}$
$= 4 \hat{i} - 12 t \hat{j}$
$∴$ angular momentum $\vec{L} = \vec{r} \times \vec{p}$
$= (2 t \hat{i} - 3 t^{2} \hat{j}) \times (4 \hat{i} - 12 t \hat{j})$
$= - 24 t^{2} \hat{k} + 12 t^{2} \hat{k}$
$= - 12 t^{2} \hat{k}$
At time $t = 2$
$\vec{L} = - 48 \hat{k}$

Stream:JEESubject:PhysicsTopic:RotationSubtopic:Angular momentum

⏱ 2mℹ️ Source: PYQ_2019

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