A particle is confined to rotate in a circula | vedclass

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

Question

(B) The angular momentum is given by $\vec{L} = \vec{r} 	imes \vec{p} = m(\vec{r} 	imes \vec{v})$. Since the particle is moving in a circular path,t

Vedclass · Accepted Answer

Only the direction of angular momentum $\vec{L}$ is conserved.

Vedclass · Answer

(B) The angular momentum is given by $\vec{L} = \vec{r} 	imes \vec{p} = m(\vec{r} 	imes \vec{v})$. Since the particle is moving in a circular path,the position vector $\vec{r}$ and velocity vector $\vec{v}$ are always perpendicular. The magnitude of angular momentum is $L = mvr$. Since the linear speed $v$ is decreasing,the magnitude of angular momentum $L$ is not conserved.However,for a particle moving in a circular path in a plane,the direction of the angular momentum vector $\vec{L}$ is perpendicular to the plane of motion (determined by the right-hand rule). As long as the particle remains in the same circular path,the direction of $\vec{L}$ remains constant.Since the particle is confined to a circular path,it cannot spiral towards the centre. Because the speed is changing,there is a tangential acceleration $a_t$ in addition to the centripetal acceleration $a_c$. Therefore,the net acceleration is not directed towards the centre. Thus,only the direction of angular momentum is conserved.

$A$ particle is confined to rotate in a circular path with decreasing linear speed. Which of the following is correct?

Similar Questions

The velocity and acceleration vectors of a particle undergoing circular motion are $\overrightarrow{v} = 2 \hat{i} \text{ m/s}$ and $\overrightarrow{a} = 2 \hat{i} + 4 \hat{j} \text{ m/s}^2$ respectively at an instant of time. The radius of the circle is $........ \text{ m}$.

$A$ particle moves in a circular path of radius $R$ with an angular velocity $\omega = a - bt$,where $a$ and $b$ are positive constants and $t$ is time. The magnitude of the acceleration of the particle after time $t = \frac{2a}{b}$ is:

If $\theta$ is the angle between the velocity vector $\vec{v}$ and the acceleration vector $\vec{a}$ of a particle moving on a circular path with decreasing speed,then .........

$A$ body is moving along a circular track of radius $100 \ m$ with velocity $20 \ m/s$. Its tangential acceleration is $3 \ m/s^{2}$,then its resultant acceleration will be (in $m/s^{2}$)

If the mass,speed,and radius of an object are increased by $50\%$,what is the percentage increase in the centripetal force?

Vedclass Test Series

Exam Paper Generator

Online Exam Module