If vec{L} and vec{P} represent the angular mo | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) Given the position vector $\vec{r} = a(\hat{i} \cos \omega t + \hat{j} \sin \omega t)$.To find the force,we first calculate the acceleration $\vec

Vedclass · Accepted Answer

Opposite to the direction of $\vec{r}$

Vedclass · Answer

(A) Given the position vector $\vec{r} = a(\hat{i} \cos \omega t + \hat{j} \sin \omega t)$.To find the force,we first calculate the acceleration $\vec{a} = \frac{d^2\vec{r}}{dt^2}$.Velocity $\vec{v} = \frac{d\vec{r}}{dt} = a\omega(-\hat{i} \sin \omega t + \hat{j} \cos \omega t)$.Acceleration $\vec{a} = \frac{d\vec{v}}{dt} = -a\omega^2(\hat{i} \cos \omega t + \hat{j} \sin \omega t) = -\omega^2\vec{r}$.Since $\vec{F} = m\vec{a}$,we have $\vec{F} = -m\omega^2\vec{r}$.This indicates that the force $\vec{F}$ is directed opposite to the position vector $\vec{r}$.

If $\vec{L}$ and $\vec{P}$ represent the angular momentum and linear momentum respectively of a particle of mass $m$ having position vector $\vec{r} = a(\hat{i} \cos \omega t + \hat{j} \sin \omega t)$,the direction of the force acting on the particle is:

Similar Questions

The angle between velocity and acceleration of a particle describing uniform circular motion is (in $^{\circ}$)

In Uniform Circular Motion ($U$.$C$.$M$.),when the time interval $\delta t \rightarrow 0$,the angle between the change in velocity $(\delta v)$ and the linear velocity $(v)$ will be (in $^{\circ}$)

$A$ scooter is going round a circular road of radius $100 \,m$ at a speed of $10 \,m/s$. The angular speed of the scooter will be ......... $rad/s$.

$A$ particle moving with uniform speed in a circular path maintains:

Two particles $A$ and $B$ are moving in uniform circular motion in concentric circles of radii $r_{A}$ and $r_{B}$ with speeds $v_A$ and $v_B$ respectively. The time period of rotation is the same. The ratio of angular speed of $A$ to that of $B$ will be

Vedclass Test Series

Exam Paper Generator

Online Exam Module