The slope of the graph of torque v/s angular acceleration will obviously give us the moment of inertia of the body and it is seen that the angular acceleration increases linearly with increasing torque. Hence we get a graph of torque v/s angular acceleration as plotted below:- Graph of torque v/s angular acceleration ![]() ![]() Suppose the moment of inertia is I=0.67kg.m 2, then Referring to the equation giving the relation of torque and the angular acceleration of the object that we have found above, we can plot a graph of torque and angular acceleration. This is the equation denoting the relationship between the torque and the angular acceleration of the object. The term mr 2 is nothing but the moment of inertia of the object extended in all dimensions of the object. Using this in the above equation, we have If the object is rotating with angular velocity ω then angular velocity is related to the angular acceleration as α=ω/t and acceleration of the object is related to the angular acceleration as Let the displacement be equal to ‘r’ from the axis of rotation then we get Θ is an angular displacement of a disc on the application of torque, ω is angular velocity and a is the acceleration of the disc. We know that the torque is a product of the force applied to the object and how far it is displaced from the applied force.Ĭonsider a circular disc of radius ‘r’ and a force F is applied on the disc to rotate it about an axis exerting a torque τ moving with angular acceleration α. ![]() The speed acquired by the object depends upon the torque applied to the body and angular acceleration is the change in the angular velocity with the time of the object rotating about an axis. The net torque acting on the object is directly proportional to the angular acceleration of the object and inversely related to the inertia of rotations about its axis of rotation. Relation between Torque and Angular Acceleration The angular acceleration of the object is due to the rotational motion of the object about its axis from the point of the center of gravity and torque is responsible for the rotational motion of the object.Īs the force is applied tangentially to the body, the equivalent force is acted on the point situated opposite to it and acts in the opposite direction that tends to rotate it with angular acceleration, and hence torque and angular acceleration both come into the picture in the case of a rotating body.
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