Three identical cylinders of radius R are in contact. Each cylinder is rotating with angular velocity w. A thin belt is moving without sliding on the cylinders. Calculate the magnitude of velocity of point P with respect to Q. P and Q are two points of belt which are in contact with the cylinder.
Answers
Given:
Three cylinders
Radius = R
Angular velocity = w
A thin belt is moving without sliding on the cylinders
P and Q are two points of belt which are in contact with the cylinder
To find:
The magnitude of velocity of point P with respect to Q
Solution:
The cylinders are rotating with the same angular velocity and the belt is moving without sliding.
Hence,
Velocity at p will be equal to the velocity at Q
By formula,
Velocity = Radius * Angular velocity
Therefore,
The velocity of P with respect to Q is 0
The velocities at P and Q are the same.
the velocity of the belt will be equal to wr....but this velocity is tangential to each sphere....on resolving it two components then by using the concept of relative velocity...we will get the answer....i.e root 3wr....