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What torque is needed to spin a spherical shell of 3000 g with a radius of 20 cm from rest to 600 rpm? The operation takes 70 seconds.

Answer :

The torque required to spin the spherical shell is 0.072 Nm.

What is torque?

Torque is a force that can cause an item to revolve around an axis. In the same way that force causes an item to accelerate in linear kinematics, torque causes an object to acquire angular acceleration. Torque is measured as a vector quantity.

Given by torque τ = Iα

Where,

I = moment of inertia

α = angular velocity

What is moment of inertia?

It is a quantitative measure of a body's rotational inertia—that is, the body's resistance to having its speed of rotation along an axis altered by the application of a torque.

We know, moment of inertia of spherical shell I = (2/3)[tex]mr^2[/tex]

Put values we get,

I = [tex](2/3)*3kg*0.20m ^2[/tex]

I = [tex]0.08 kgm^2[/tex]

To find angular acceleration α = change in angular velocity / time

= 600 rpm / 70 s

= 10 rps / 70

= 0.143 [tex]revolutions/s^2[/tex]

= 0.143*6.28319

= 0.897598 [tex]radian/s^2[/tex]

α = 0.898 [tex]radian/s^2[/tex]

Torque τ = 0.08*0.898 = 0.0718 Nm ≅ 0.072 Nm

The torque required to spin the spherical shell is 0.072 Nm.

To know more about torque, check out:

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