Answer to Question #95749 in Mechanical Engineering for Kshamaa.S

Question

A 10kg cylinder of radius 8 cm is rotating in a symmetric
V - channel with angular velocity 3.14 rads
-1
. Write the free
body diagram and calculate the torque required to keep it
rotating with the same angular velocity?
Given: The co-efficient of friction between the cylinder and
the surface = 0.3.

Answer 1

The torque is given by formula

where I is the moment of inertia, ε is angular acceleration

In our case, the moment of inertia is equal to

The angular acceleration is given by formula

Cylinder moves only under friction, and we can write according to the Second Law of Newton

Using (4) we get

We put (5) in (3)

We put (2) and (6) in (1)

Using (7) we get: M=24

Answer

24