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Relationship Between The Torque And The Angular Acceleration In a Form Of Equation

Referencing Styles : Chicago | Pages : 1

Torque and angular acceleration are interlinked with each other by a formula. Torque is related with the objects moment of inertia. It can be stated that when a body experiences the torque it is seen that the object starts rotating with an acceleration which is inversely proportional to the moment of inertia. The relation between the torque and angular acceleration can be stated as the Newton’s Second Law related to rotation. However, the angular acceleration which is observed follows the Newton’s First Law. In order to understand the relation between torque and angular acceleration, it is important to know what they are actually. Torque can be stated as the rotating or the twisting effect of a force. The S.I unit of torque is Newton-meter which can be denoted as ‘Nm’. The change in the rate of the velocity is known as the angular acceleration. It can be stated that it is represented by ‘a’.

 

The above diagram can easily be used to study the relationship between torque and angular momentum.  Assume that a mass ‘m’ is moving in a circular path having the radius ‘r’, a force which is tangential is acting upon it which is denoted by Ft as illustrated in the figure above. However, using Newton’s Second law a relation can be established between Ft with the tangential acceleration which is at = rα, where the term ‘α’ denotes the angular acceleration.

Ft = mat = mrα

 The torque at the centre of rotation is due to the Ft  can be stated as: Torque is equal to tangential force multiplied by the radius of the circular path. Therefore, it can be stated that

τ = mr^2*α

The above equation helps in establishing the relationship between torque and the angular acceleration. It can be stated that when a torque is applied on an object it starts rotating with an acceleration. The acceleration is inversely proportional to the moment of inertia. The moment of inertia need to be elaborated in the same way like the torque is defined with the help of a particular axis. The choice of the axis can differ for different cases. The main factor upon which the moment of inertia depends is upon the mass. The mass which is distributed long a particular axis. In case of a given total mass it is observed that the moment of inertia always depends or rather rely on how the mass is distributed among the given axis. It is observed that the moment of inertia is always greater if the mass is moved further away from the axis. If the mass is distributed closer to the axis than the moment of inertia is comparatively less. It is often observed that the rotational velocity decreases stating that the acceleration cannot be zero. It can be easily concluded that it is not necessary that if an object is a rotating object and it is in translational equilibrium it is not mandatory that the object will also be in rotational equilibrium. However, the Newton’s Law is used to establish relationship between torque and angular acceleration.

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