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