Zeeshan asked in Science & MathematicsPhysics · 8 years ago

# why v=w*r is correct equation explain with diagrame?

IN TOPIC OF RELATION BETWEEN ANGULAR AND LENIER VELOCIT What is correct equation in v=rw/v=w*r and why explain with diagrame.Please!

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• 8 years ago

Hello Zeeshan, v = r w as we consider only the magnitudes.

As we write in the form of vectors, then v vector = w vector X r vector.

X stands for cross product of vectors.

It is very simple dear.

Assume a body going round a circular path of radius r

Draw yourself a circle of radius say 5cm

Now mark two points on the circle so close to each other and name the points as A and B

Join those with the centre O of the circle. Mark the angle AOB as d@

Let AB be marked as ds

Let ds be the distance covered in a short time duration dt. And in the same dt the radius OA has swept an angle d@ at O.

Now by sector formula Arc length = radius of curvature x angle subtended at the centre

Hence ds = r d@

Now divide both sides by dt

So ds/dt = r d@/dt

By definition ds/dt is the linear velocity v and d@/dt is the angular velocity w

Hence v = r w

[Recall 2pir (biggest arc in the circle) = r * 2pi

you know 2pi is the angle subtended by the whole circle at the centre].

• 8 years ago

What diagrame?

No picture as promised, no answer.