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

$M=I ε (1)$

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

In our case, the moment of inertia is equal to

$I=mr^2 (2)$

The angular acceleration is given by formula

$ε=\frac {a}{r} (3)$

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

$µmg=ma (4)$

Using (4) we get

$a=µg (5)$

We put (5) in (3)

$ε=\frac {µg}{r} (6)$

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

$M= mr^2×\frac {µg}{r} = mrµg (7)$

Using (7) we get: M=24

Answer

24