two equal and opposite forces are applied tangentially to a uniform disc of mass M and radius R. If the disc is pivoted at its centre and free to rotate in its plane,then find its angular acceleration.
Answers
Torque is equal to Linear Force times Radius
T = F*R
Since equal forces are applied on the disc in opposite directions,
The resultant torque = T = FR – (-FR) = 2FR ------------ Equation1.
In circular motion, torque (T) is required to produce an angular acceleration (α) of an object.
The amount of torque required to produce an angular acceleration (α) depends on the distribution of the mass (m) of the disc. From laws of circular motion,
torque = (moment of inertia)(angular acceleration)
T = I * α
I = moment of inertia, this is a value that describes the distribution.
α = angular acceleration
The moment of inertia of a solid disc is ½MR²
where M is the mass of the disc, and R is the radius.
T = MR²*α/2 ------------------------Equation2
From Equation1 and Equation2, we equate
2FR = MR²*α/2
Angular acceleration = α = 4F/MR
The answer is provided in the attachment.
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