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Question
Obtain an expression for torque acting on a body rotating with uniform angular acceleration.
Solution
Expression for torque acting on a rotating body
a) Suppose a rigid body consists of n particles of masses m1, m2, m3, ......, mn which are situated at distances r1, r2, r3, …, rn respectively, from the axis of rotation as shown in figure
b) Each particle revolves with angular acceleration α
c) Let F1, F2, F3, …., Fn be the tangential force acting on particles of masses, m1, m2, m3, …, mn respectively.
d) Linear acceleration of particles of masses m1, m2,…, mn are given by, a1 = r1 α, a2 = r2α, a3 = r3α= rnα
e) Magnitude of force acting on particle of mass m1 is given by F1 = m1a1 = m1r1α [ a = rα]
Magnitude of torque on particle of mass m1 is given by,
t1 = F1 r1 sin Θ [∵ Radius vector is ⊥ar to tangential force]
Thus, when a torque rotates the body with uniform angular acceleration of 1 rad/s2 then M.I of the body about a given axis of rotation becomes equal to torque acting on it.
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