Circular Motion

Let is the angle made by the wire with the vertical.

Here,  .

From the physics perspective, in uniform circular motion, speed and angular velocity are constant. That makes the angular acceleration and tangential acceleration are zero. Non-uniform motion, on the other hand, has varying speed and angular velocity, where angular acceleration is non-zero. 

The period T is the time taken to complete one full revolution (2? radians). In uniform circular motion, it relates to angular velocity by? =2? /T and to tangential speed by v=? r=2? r/T .

The principle of circular motion follows Newtonian mechanics. It can be stated that an object will move in a circle only when there is a centripetal force that continuously acts perpendicular to its tangential velocity. That changes the direction but not its speed. The inward acceleration a_c = v squared/r obeys Newton's laws and ensures circular path motion. 

Circular motion has the following characteristics.

• Fixed radius with the same and constant distance from the centre
• Constant speed, when the motion is uniform
• A changing velocity vector with continuous direction of change
• Centripetal acceleration that is directed radially inwards, while the force that causes it is the centripetal force that maintains the curved path

By N L M : T sin θ = ${}^{}$  $m{\omega }^{2}R$ - (1)

& R = $\mathcal{l}$ $$ sin θ - (2)

From (1) & (2)

$\Rightarrow Tsin\theta =m{\omega }^2\mathcal{l}sin\theta$

$\Rightarrow T=m{\omega }^2\mathcal{l}$

$\Rightarrow 80=\left(\frac{100}{1000}\right){\omega }^2*2$

$\Rightarrow \frac{800}{2}={\omega }^2$

$\Rightarrow {\omega }^2=400$

$\omega =20rad/sec$

And, $\omega =\frac{2\pi N}{2\pi }$ $\frac{}{}$

$N=\frac{20*60}{2\pi }$

$N=\frac{600}{\pi }rpm=\frac{k}{\pi }$