The magnitude of displacement of a particle m | vedclass

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

Question

If a particle is moving with angular velocity $=\omega$

Its angle of rotation is given by $\omega t$

Now displacement $=$ length of line $A B$

Vedclass · Accepted Answer

$2a\, sin \frac{{\omega \,t}}{2}$

Vedclass · Answer

If a particle is moving with angular velocity $=\omega$

Its angle of rotation is given by $\omega t$

Now displacement $=$ length of line $A B$

Position vector of a particle is given by

$\vec{R}=i a \cos \omega t+j a \sin \omega t$

$\vec{R}_{0}=a i$

displacement$, \vec{d}=\vec{R}-\vec{R}_{\mathrm{o}}$

$=a(\cos \omega t-1) i+a \sin \omega j$

$d=\sqrt{(a(\cos \omega t-1))^{2}+(a \sin \omega)^{2}}$

$=a \sqrt{2(1-\cos \omega t)}=a \sqrt{2 	imes 2(\sin \omega t / 2)^{2}}=2 a \sin \omega t / 2$

The magnitude of displacement of a particle moving in a circle of radius $a$ with constant angular speed $\omega$ varies with time $t$ as

Similar Questions

A child is standing at one end of a long trolley moving with a speed $v$ on a smooth horizontal floor. If the child starts running towards the other end of the trolley with a speed $u$, the centre of mass of the system (trolley + child) will move with a speed.

A particle originally at rest at the highest point of $a$ smooth vertical circle is slightly displaced. It will leave the circle at $a$ vertical distance $h$ below the highest point, such that

Two disc one of density $7.2\, g/cm^3$ and the other of density $8.9\, g/cm^3$ are of same mass and thickness. Their moments of inertia are in the ratio

A disc is rotating with an angular velocity $\omega_0$. A constant retarding torque is applied on it to stop the disc. The angular velocity becomes $\frac{{{\omega _0}}}{2}$ after $n$ rotations. How many more rotations will it make before coming to rest

A force $\vec F$ acts on a particle having position vector $\vec r$ (with respect to origin). It produces a torque $\vec \tau $ about origin, choose the correct option