Make Note of Newton’s Second Law of Rotation

In the second law of rotation, Newton has specifically limited the rotational equation of a rotating object based on a singular principal axis. Following this fact, the current study has intended to represent an overview that casts light on the explanation of Newton’s second law of rotation. In addition, the study will include further information based on the application and examples of that particular concept of physics as well. 

Explanation of Newton’s Second Law of Rotation

The second law of Newton, based on the rotation, has stated that if on a rigid body with a fixed axis, one or more than one torque is applied the sum of the torques will be equivalent to the moment of inertia times the regular acceleration. For instance, it can be conjectured that a rigid body is rotating about an axis that is fixed. In the same condition, multiple forces are acting on it in order to change the angular velocity.  Following this scenario, all the particles of the rigid body will complete their circular motion together and the angular acceleration of all particles will have no difference. 

Examples Regarding Newton’s Second Law of Rotation

In order to analyse the rotational motion of a rod displays two kinds of forces that are acting on it. The forces are Mg, which refers to the gravitational force that acts at the centre of the gravity of the rod. Another factor is represented by F, which refers to the factor that is created due to the hinge on the rod.  The moment of inertia of the rod is referred to as I about an axis passing through the hinge. Therefore, following the scenario, the perpendicular to the rod is ML2/3. 

Basic Formula of Newton’s Second Law of Rotation

Based on the statement of Newton’s second law of rotation, the basic formula has been developed that has been represented as ∑iτi=Iα. In this formula, the term Iα has been stated as a scalar quantity and can have both kinds of values, negative or positive that refer to the rotational angle such as clockwise or counter clockwise. Therefore, if it can be conjectured that an object rotates clockwise, it will experience a torque that is positive. Therefore, the angular acceleration of the rotating object will be positive as well. 

Application of Newton’s Second Law of Rotation

Based on the examples and the discussion based on the second law of Newton of rotation, a particular application of the formula is represented in this section. Suppose, a wooden disk of mass (m) and radius (R) has a string of negligible mass. This will be wrapped about it. In this scenario, if the disk is allowed to fall while holding the string, the acceleration (a) of the wooden disk will be ⅔ g. The phenomenon has stated that the direction will be positive and downward so the equation will be Mg-T=ma and there will be no torque from gravity. 

Deriving Second Law of Newton for Rotation in Vector Form

The formula of the second law of the rotation reveals the relation between the change of transitional motion of an object and the net force. Based on this scenario, by relating the angular acceleration to the position, the tangential acceleration vectors will be a=α×r. Using the cross product identity that is (r) the equation will be represented as Σ(r×→F)=r×(ma)=mr×→a=mr2a.

Problem Solving Strategy of the Second Law derived by Newton for Rotation 

• The system of the interest needs to be determined
• In order to be sanguine about the inclusion of the mass and torque in the rotation, a pre-examination is needed to be conducted
• Drawing of the situation helps to understand the scenarios that are stated in the problem and helps in identifying the pivot point as well
•  Application of ∑iτi=Iα is considered an important action in order to solve the given problem

Conclusion

In this study, the second law of Newton of rotation has been exemplified in a brief manner. The study further includes the strategies that need to be determined while solving any problem that includes the formula regarding the second law of the rotation. The application of the formula of Newton’s second law of rotation has been stated to represent an example of a problem that can include the formula ∑iτi=Iα. In addition to the explanation of this particular formula, the study includes further explanations related to the vector form of the angular rotation.