Question #95749

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.

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.

Expert's answer

The torque is given by formula

"M=I \u03b5 (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

"\u03b5=\\frac {a}{r} (3)"

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

"\u00b5mg=ma (4)"

Using (4) we get

"a=\u00b5g (5)"

We put (5) in (3)

"\u03b5=\\frac {\u00b5g}{r} (6)"

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

"M= mr^2\u00d7\\frac {\u00b5g}{r} = mr\u00b5g (7)"

Using (7) we get: M=24

Answer

24

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