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proof torque=i alpha,where i is the moment of inertia and alpha is the angular acceleration.

proof torque=i alpha,where i is the moment of inertia and alpha is the angular acceleration.

Grade:12

1 Answers

Arun
25763 Points
2 years ago
The force acting on a particle of mass m1 situated at A, at a distance r1, from the axis of rotation = mass x acceleration
 
= m1 x  d/dt(r1ω)
 = (m1 r1)dω /dt
= (m1 r1)d2θ/dt2
The moment of this force about the axis of rotation
= Force x  perpendicular distance 
= (m1 r1)d2θ/dt2   x r1
Therefore, the total moment of all the forces acting on all the particles 
or τ = Iα
where ∑ m1r12 = moment of inertia I of the rigid body and α = d2 θ /dt2 angular acceleration.
 

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