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!
- trueproberLv 78 years agoFavorite Answer
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].
- gintableLv 78 years ago
No picture as promised, no answer.
- Anonymous8 years ago
try asking myphysicsbuddy, that may help, if found online