derive the formula of torque in term of MLT
Answer (1)
Student Expert
17th Jan, 2021
Torque (T) = Moment of Inertia Angular Acceleration . . . . (1)
Since, Moment of Inertia (M.O.I) = Radius of Gyration 2 Mass
The dimensional formula of Moment of Inertia = M 1 L 2 T 0 . . . (2)
And, Angular Acceleration = Angular velocity Time -1
The dimensional formula of Angular Acceleration = M 0 L 0 T -2 . . . (3)
On substituting equation (2) and (3) in equation (1) we get,
Torque = Moment of Inertia Angular
Acceleration
Or, I = [M 1 L 2 T 0 ] [M 0 L 0 T -2 ] = [M L 2 T -2 ].
Therefore, the torque is dimensionally represented as [M L 2 T -2 ].
Since, Moment of Inertia (M.O.I) = Radius of Gyration 2 Mass
The dimensional formula of Moment of Inertia = M 1 L 2 T 0 . . . (2)
And, Angular Acceleration = Angular velocity Time -1
The dimensional formula of Angular Acceleration = M 0 L 0 T -2 . . . (3)
On substituting equation (2) and (3) in equation (1) we get,
Torque = Moment of Inertia Angular
Acceleration
Or, I = [M 1 L 2 T 0 ] [M 0 L 0 T -2 ] = [M L 2 T -2 ].
Therefore, the torque is dimensionally represented as [M L 2 T -2 ].
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