Newton

1
Newtons Laws of Motion Applicable to Angular
Motion

• Dr. Ajay Kumar
• Professor
• School of Physical Education
• DAVV Indore

2
Newton's Laws and Angular Motion

• 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 objects center of
  gravity. 

3

• 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.

4

• 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.

5
First Law

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

6

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

7

• 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). 

8

• 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.

9
Second Law

• 2nd 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.

10

• 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.

11

• 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).

12
Law of Conservation of Angular Momentum

• Newtons 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. 
•  

13

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

14
Third Law

• 3rd 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 Newtons 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. 

15

• 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).

16
Transfer of momentum

• 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. 

17

• 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.