Newton’s Laws of Motion Newton’s Laws of Motion Applicable to Angular Applicable to Angular

MotionMotion

Dr. Ajay KumarDr. Ajay Kumar

ProfessorProfessor

School of Physical EducationSchool of Physical Education

DAVV IndoreDAVV Indore

Newton's Laws and Angular MotionNewton's Laws and Angular Motion

With slight modification, Newton's With slight modification, Newton's laws of linear motion can  be applied laws of linear motion can  be applied to angular motion. to angular motion.

An eccentric force will result in An eccentric force will result in rotation, provided the body is freely rotation, provided the body is freely moving.moving.

Eccentric force: A force which is Eccentric force: A force which is applied off center. In other words, the applied off center. In other words, the direction of the force is not in line with direction of the force is not in line with the object’s center of gravity.  the object’s center of gravity. 

External forces applied to the human External forces applied to the human body are typically eccentric.body are typically eccentric.

Rotatory motion of a lever usually Rotatory motion of a lever usually results when muscle pulls on bone, results when muscle pulls on bone, providing the external resistance is providing the external resistance is less than the amount of muscular less than the amount of muscular force acting on the bone. force acting on the bone.

When observing segmental motion of When observing segmental motion of the human body, muscle force is the human body, muscle force is considered an external force. considered an external force. 

If you consider  the entire body If you consider  the entire body undergoing general motion, muscle undergoing general motion, muscle forces would be considered an forces would be considered an internal force. internal force.

First LawFirst Law

1st Law: A body continues in a state 1st Law: A body continues in a state of rest or uniform  rotation about its of rest or uniform  rotation about its axis unless acted  upon by an axis unless acted  upon by an external torque.external torque.

Angular Inertia (I ; Moment of inertia) is Angular Inertia (I ; Moment of inertia) is the sum of all the masses (m) multiplied the sum of all the masses (m) multiplied by the radius squared (r2). by the radius squared (r2).                        

I =    (m)(r2) I =    (m)(r2) If the mass is concentrated farther away If the mass is concentrated farther away

from the axis  of rotation, the moment of from the axis  of rotation, the moment of inertia will  be greater, thus the system inertia will  be greater, thus the system (i.e., lever)  will be harder to start or stop. (i.e., lever)  will be harder to start or stop.

The greater the moment of inertia, The greater the moment of inertia, the more difficult it is for an external the more difficult it is for an external torque to change the state of rest or torque to change the state of rest or uniform motion of a rotating body. uniform motion of a rotating body.

In regards to the human body, the In regards to the human body, the mass distribution about an axis of mass distribution about an axis of rotation (i.e., joint) may be altered by rotation (i.e., joint) may be altered by changing the limb position (i.e., changing the limb position (i.e., bringing the limb in closer to the axis bringing the limb in closer to the axis of rotation by flexing at a joint).  of rotation by flexing at a joint). 

As a human locomotors, angular inertia As a human locomotors, angular inertia (moment of inertia) varies.  (moment of inertia) varies. 

For example,  a jogger is able to recover the For example,  a jogger is able to recover the leg faster by tucking the foot close to the leg faster by tucking the foot close to the buttocks.  buttocks. 

The jogger has concentrated the mass of The jogger has concentrated the mass of the leg closer to the axis of rotation (hip the leg closer to the axis of rotation (hip joint) which decreases the moment of joint) which decreases the moment of inertia and therefore increases the rate at inertia and therefore increases the rate at which the leg is recovered. which the leg is recovered.

Second LawSecond Law

2nd Law: The acceleration of a rotating 2nd Law: The acceleration of a rotating body is directly  proportional to the body is directly  proportional to the torque causing it, is in the  same torque causing it, is in the  same direction of the torque and is inversely direction of the torque and is inversely proportional to the moment of inertia. proportional to the moment of inertia.

Angular acceleration is the torque Angular acceleration is the torque divided by  the moment of inertia. divided by  the moment of inertia.

Angular acceleration is also the change Angular acceleration is also the change in  angular velocity divided by time. in  angular velocity divided by time.

Angular momentum is the force Angular momentum is the force needed to start or stop rotational needed to start or stop rotational motion. motion.

Angular momentum is the product of Angular momentum is the product of angular  velocity and moment of angular  velocity and moment of inertia. inertia.

The greater the angular momentum, The greater the angular momentum, the greater the force needed to stop the greater the force needed to stop the motion. the motion.

Using a heavier bat will result in a greater Using a heavier bat will result in a greater angular momentum provided that angular angular momentum provided that angular velocity is maintained.  velocity is maintained. 

Also, increasing the angular velocity of a Also, increasing the angular velocity of a bat will increase the angular momentum.  bat will increase the angular momentum. 

Angular momentum of a limb is increased Angular momentum of a limb is increased if the angular velocity is increased (i.e., if the angular velocity is increased (i.e., kicking a ball). kicking a ball).

Law of Conservation of Angular Law of Conservation of Angular MomentumMomentum

Newton’s first law can be related to Newton’s first law can be related to angular momentum.  angular momentum. 

The angular momentum associated The angular momentum associated with a  rotating body remains with a  rotating body remains constant unless influenced by external constant unless influenced by external torques.  torques. 

Divers, dancers,  figure skaters make Divers, dancers,  figure skaters make use of this law.  use of this law. 

   

For example, a diver will change For example, a diver will change from a lay out position to a tucked from a lay out position to a tucked position in order to increase position in order to increase angular rotation (angular velocity).  angular rotation (angular velocity). 

The tuck position results in a The tuck position results in a reduced moment of inertia. since reduced moment of inertia. since angular momentum is conserved, angular momentum is conserved, angular velocity must increaseangular velocity must increase

Third LawThird Law

3rd Law:    When a torque is applied by one 3rd Law:    When a torque is applied by one body to another, the  second body will  exert body to another, the  second body will  exert an equal and opposite torque  on the other an equal and opposite torque  on the other body. body.

Body movements which serve to  regain Body movements which serve to  regain balance are explained by Newton’s third law.  balance are explained by Newton’s third law. 

This is evident in gymnasts. If a gymnast This is evident in gymnasts. If a gymnast lowers the left arm downward,  the right arm lowers the left arm downward,  the right arm will react move upward (actually moving will react move upward (actually moving opposite the left arm) to maintain balance and opposite the left arm) to maintain balance and therefore prevent falling from the balance therefore prevent falling from the balance beam.  beam. 

Going from a tight tuck to a lay out Going from a tight tuck to a lay out position, the diver rotates the trunk position, the diver rotates the trunk back (extends the trunk). The back (extends the trunk). The reaction is for the lower extremities reaction is for the lower extremities to rotate the opposite direction to rotate the opposite direction (extention at the hips). (extention at the hips).

Transfer of momentumTransfer of momentum

Angular momentum can be transferred Angular momentum can be transferred from one body segment to the next.  from one body segment to the next. 

Since body segments differ in mass, Since body segments differ in mass, the moment of inertia of each body will the moment of inertia of each body will vary.  vary. 

Considering that momentum is Considering that momentum is conserved, a reduction in the moment conserved, a reduction in the moment of inertia of a body part will result in of inertia of a body part will result in an increased angular velocity.  an increased angular velocity. 

The latter can be applied to throwing The latter can be applied to throwing and kicking movements. For example, and kicking movements. For example, throwing involves a series of angular throwing involves a series of angular rotations of progressively lighter body rotations of progressively lighter body segments (leg/trunk--arm). segments (leg/trunk--arm).

A reduction in moment of inertia A reduction in moment of inertia between the leg/trunk complex and between the leg/trunk complex and the lighter arm, results in an the lighter arm, results in an increased velocity of the arm. increased velocity of the arm.