Newtons Laws of Motion Applicable to Angular Motion

Newton’s Laws of Motion Applicable to Angular Motion Dr. Ajay Kumar Professor School of Physical Education DAVV Indore

Newton's Laws and Angular Motion n With slight modification, Newton's laws of linear motion can be applied to angular motion. An eccentric force will result in rotation, provided the body is freely moving. Eccentric force: A force which is applied off center. In other words, the direction of the force is not in line with the object’s center of gravity.

n n External forces applied to the human body are typically eccentric. Rotatory motion of a lever usually results when muscle pulls on bone, providing the external resistance is less than the amount of muscular force acting on the bone.

n n When observing segmental motion of the human body, muscle force is considered an external force. If you consider the entire body undergoing general motion, muscle forces would be considered an internal force.

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

n n Angular Inertia (I ; Moment of inertia) is the sum of all the masses (m) multiplied by the radius squared (r 2). I = (m)(r 2) If the mass is concentrated farther away from the axis of rotation, the moment of inertia will be greater, thus the system (i. e. , lever) will be harder to start or stop.

n n The greater the moment of inertia, the more difficult it is for an external torque to change the state of rest or uniform motion of a rotating body. In regards to the human body, the mass distribution about an axis of rotation (i. e. , joint) may be altered by changing the limb position (i. e. , bringing the limb in closer to the axis of rotation by flexing at a joint).

n n n As a human locomotors, angular inertia (moment of inertia) varies. For example, a jogger is able to recover the leg faster by tucking the foot close to the buttocks. The jogger has concentrated the mass of the leg closer to the axis of rotation (hip joint) which decreases the moment of inertia and therefore increases the rate at which the leg is recovered.

Second Law n n n 2 nd Law: The acceleration of a rotating body is directly proportional to the torque causing it, is in the same direction of the torque and is inversely proportional to the moment of inertia. Angular acceleration is the torque divided by the moment of inertia. Angular acceleration is also the change in angular velocity divided by time.

n n n Angular momentum is the force needed to start or stop rotational motion. Angular momentum is the product of angular velocity and moment of inertia. The greater the angular momentum, the greater the force needed to stop the motion.

n n Using a heavier bat will result in a greater angular momentum provided that angular velocity is maintained. Also, increasing the angular velocity of a bat will increase the angular momentum. Angular momentum of a limb is increased if the angular velocity is increased (i. e. , kicking a ball).

Law of Conservation of Angular Momentum n n n Newton’s first law can be related to angular momentum. The angular momentum associated with a rotating body remains constant unless influenced by external torques. Divers, dancers, figure skaters make use of this law.

For example, a diver will change from a lay out position to a tucked position in order to increase angular rotation (angular velocity). n The tuck position results in a reduced moment of inertia. since angular momentum is conserved, angular velocity must increase n

Third Law n n n 3 rd Law: When a torque is applied by one body to another, the second body will exert an equal and opposite torque on the other body. Body movements which serve to regain balance are explained by Newton’s third law. This is evident in gymnasts. If a gymnast lowers the left arm downward, the right arm will react move upward (actually moving opposite the left arm) to maintain balance and therefore prevent falling from the balance beam.

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

Transfer of momentum n n n Angular momentum can be transferred from one body segment to the next. Since body segments differ in mass, the moment of inertia of each body will vary. Considering that momentum is conserved, a reduction in the moment of inertia of a body part will result in an increased angular velocity.

n n The latter can be applied to throwing and kicking movements. For example, throwing involves a series of angular rotations of progressively lighter body segments (leg/trunk--arm). A reduction in moment of inertia between the leg/trunk complex and the lighter arm, results in an increased velocity of the arm.