MOMENT OF FORCEMOMENT OF FORCE

Dr. Ajay Kumar Dr. Ajay Kumar

School of Physical EducationSchool of Physical Education

DAVV IndoreDAVV Indore

Introduction and conceptIntroduction and concept

In addition to linear forces in which all forces In addition to linear forces in which all forces occurs along the same action line,occurs along the same action line,

Or Or The concurrent force in which force acting at The concurrent force in which force acting at

different angles are applied at the same different angles are applied at the same point.point.

Another situation exist in which force not act Another situation exist in which force not act in the same action line but parallel to each in the same action line but parallel to each other act at different points on a body.other act at different points on a body.

These forces are known as parallel forces.These forces are known as parallel forces.

Cont.Cont.

The effects of parallel forces on a body The effects of parallel forces on a body depends on the magnitude, the direction, depends on the magnitude, the direction, and application point of each other.and application point of each other.

Parallel forces may act in the same or Parallel forces may act in the same or opposite direction. opposite direction.

They may be balanced and cause no They may be balanced and cause no motion or motion or

They may cause linear or rotatory They may cause linear or rotatory motion.motion.

Cont.Cont.

If we exert equal and opposite forces If we exert equal and opposite forces rotatory motion about the center of rotatory motion about the center of gravity of the weight will occur.gravity of the weight will occur.

The effect of equal parralel force The effect of equal parralel force acting in opposite direction is called acting in opposite direction is called a couple or force couple.a couple or force couple.

Example : Steering of the if Example : Steering of the if controlled by both hands.controlled by both hands.

Cont.Cont.

The turning effect of a force is called The turning effect of a force is called torque or moment of force.torque or moment of force.

The torque about any point equals The torque about any point equals the product of the force magnitude the product of the force magnitude and its perpendicular distance from and its perpendicular distance from point of application of force to the point of application of force to the point of axis of rotation.point of axis of rotation.

Cont.Cont.

The perpendicular distance is called The perpendicular distance is called the moment arm or torque arm.the moment arm or torque arm.

Since a force moment is the product Since a force moment is the product of force and moment arm length, it of force and moment arm length, it may be increased or decreased by may be increased or decreased by increasing or decreasing either the increasing or decreasing either the force or the force arm length.force or the force arm length.

Cont.Cont.

In human body the mass or weight of In human body the mass or weight of a segment cannot be altered, a segment cannot be altered, therefore the torque of a segment therefore the torque of a segment due to gravitational force can only be due to gravitational force can only be changed by changing the length of changed by changing the length of the momnet arm in relation to the the momnet arm in relation to the axis.axis.

Moment of InertiaMoment of Inertia

The quality of a body to resist change in The quality of a body to resist change in its state of motion or rest was identified its state of motion or rest was identified as inertia.as inertia.

The inertia of a body with respect to the The inertia of a body with respect to the linear motion was shown to be directly linear motion was shown to be directly proportional to the mass of the object.proportional to the mass of the object. The heavier the object the more force it The heavier the object the more force it

takes to start it moving and more force to takes to start it moving and more force to stop it.stop it.

Cont.Cont.

This is also true in rotatory motion.This is also true in rotatory motion. The amount of force needed to start The amount of force needed to start

or stop a spinning object is related to or stop a spinning object is related to its mass.its mass.

But practically we can easily feel that But practically we can easily feel that to start a hammer moving in a to start a hammer moving in a circular motion or to stop a moving circular motion or to stop a moving hammer in a circular fashion is hammer in a circular fashion is difficult.difficult.

Cont.Cont.

Therefore it seem that hammer Therefore it seem that hammer inertia is greater when moving in an inertia is greater when moving in an angular pattern than moving in a angular pattern than moving in a linear path.linear path.

Since the mass of the hammer does Since the mass of the hammer does not change, this increase in inertia not change, this increase in inertia must be due to some other factor.must be due to some other factor.

Cont.Cont.

In the same way the torque causing In the same way the torque causing rotatory motion is dependent upon rotatory motion is dependent upon the magnitude of the force and the the magnitude of the force and the perpendicular distance from the line perpendicular distance from the line of action to the force to the axis, the of action to the force to the axis, the inertia of a rotatory body is affected inertia of a rotatory body is affected by the distance between the mass by the distance between the mass and the axis of rotation.and the axis of rotation.

Cont.Cont.

As the distance between the axis and As the distance between the axis and the mass increases, the inertia the mass increases, the inertia increases.increases.

THIS ANGULAR INERTIA IS CALLED THIS ANGULAR INERTIA IS CALLED THE MOMENT OF INERTIA (I)THE MOMENT OF INERTIA (I)

Cont.Cont.

The exact nature of this relationship The exact nature of this relationship is shown in the equation for the is shown in the equation for the moment of inertiamoment of inertia

I = ∑mrI = ∑mr22

Where m is the mass of the object and r Where m is the mass of the object and r is the perpendicular distance between is the perpendicular distance between mass and axis of rotation.mass and axis of rotation.