Transcript Slide 1 - School of Physical Education

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
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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.
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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.
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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
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1st Law: A body continues in a state of
rest or uniform rotation about its axis
unless acted upon by an external torque.
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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.
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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).
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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
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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.
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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.
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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
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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).
 The tuck position results in a reduced
moment of inertia. since angular
momentum is conserved, angular
velocity must increase
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Third Law
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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 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.
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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
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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.
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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.