In circular motion,the centripetal accelerati | vedclass

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

Question

(B) In circular motion,the velocity vector $\vec{v}$ is related to the angular velocity vector $\vec{\omega}$ and the position vector $\vec{r}$ by the

Vedclass · Accepted Answer

$\vec \omega 	imes \vec v$

Vedclass · Answer

(B) In circular motion,the velocity vector $\vec{v}$ is related to the angular velocity vector $\vec{\omega}$ and the position vector $\vec{r}$ by the relation $\vec{v} = \vec{\omega} 	imes \vec{r}$.The acceleration vector $\vec{a}$ is the time derivative of the velocity vector: $\vec{a} = \frac{d\vec{v}}{dt} = \frac{d}{dt}(\vec{\omega} 	imes \vec{r})$.Using the product rule for differentiation,we get $\vec{a} = \frac{d\vec{\omega}}{dt} 	imes \vec{r} + \vec{\omega} 	imes \frac{d\vec{r}}{dt}$.Since $\frac{d\vec{\omega}}{dt} = \vec{\alpha}$ (angular acceleration) and $\frac{d\vec{r}}{dt} = \vec{v}$,we have $\vec{a} = \vec{\alpha} 	imes \vec{r} + \vec{\omega} 	imes \vec{v}$.For uniform circular motion,the angular acceleration $\vec{\alpha} = 0$,so the acceleration is purely centripetal: $\vec{a}_c = \vec{\omega} 	imes \vec{v}$.

In circular motion,the centripetal acceleration is given by

Similar Questions

The net applied force on a body in uniform circular motion should always be

The distance of a particle moving on a circle of radius $12 \, m$ measured from a fixed point on the circle and measured along the circle is given by $s = 2t^3$ (in meters). The ratio of its tangential to centripetal acceleration at $t = 2 \, s$ is .........

The force required to keep a body in uniform circular motion is:

$A$ cyclist is riding with a speed of $36 \,km/h$. As he approaches a circular turn on the road of radius $50 \,m$, he applies brakes and reduces his speed at the constant rate of $0.5 \,m/s^2$. The magnitude and direction of the net acceleration of the cyclist on the circular turn are respectively:

Explain the effects of the radial component and the tangential component of the linear acceleration of a particle in circular motion.

Vedclass Test Series

Exam Paper Generator

Online Exam Module