Torque

Torque:-

The turning effect produced by a force acting on a body around an axis or point is called ‘Torque’.

Mathematically torque can be defined as the product of force applied and its perpendicular distance from the center axis.

S.I unit of torque is N-m (Newton-meter)

Centripetal and Centrifugal Forces

Centripetal and Centrifugal forces:-

Centripetal and Centrifugal forces are two equal and opposite forces acting on a body moving in a defined circular or elliptical path.

A stone tied with a thread rotated in a circular path is the best example of centrifugal and centripetal forces. The rotating motion of stone produces a force due to moment of inertia, which acts radially outwards, is called ‘Centrifugal Force’.

-Similarly an equal and opposite force is produced through the thread which acts inwards and stops the stone getting  thrown out in the air due to centrifugal force. This equal and opposite force is called ‘Centripetal Force’.

A balance between centrifugal and centripetal force is necessary for continuous and defined circular motion of stone. If we increase the rotational speed of stone beyond a certain limit, the thread will reach upto its maximum tension and get broken. And the stone will be thrown out in the air.

For Example:-

Rotation of planets around sun: - All planets are rotating in a defined elliptical path due to balanced centrifugal and centripetal forces. The gravitational force between planet and sun acts as centripetal force in order to balance the centrifugal force produces by the motion of planet.

Centrifugal force =  mass x angular acceleration

                                            =   m × ω²r

                                                 =  m ω²r

Couple of Forces

Couple:-

Two Parallel forces with equal magnitude but acting in opposite directions are called as ‘Couple’.

A couple acting on a body produce rotary motion in the body.

Moment Of Force

Moment of Forces:-

When force is applied on body which is free to rotate about a fulcrum point, a rotational moment is produced by the applied force. This rotational effect produced is called ‘Moment of force’.

Mathematically it can be expressed as the product of Force applied and the perpendicular distance of force from the fulcrum point.

i)

ii)    

Momentum

If a body with mass 'm' is moving with velocity 'v'. The momentum of the body can be expressed as the product of mass and velocity.

Momentum = mass x velocity

Angular Displacement, Velocity & Acceleration

a) Angular Displacement:-  
Change in angular position of an object with respect to time is called 'Angular Displacement'.

b) Angular Velocity:- 

Rate of change of angular displacement with respect to time is called ' Angular Velocity'. Angular velocity is denoted by     (Omega).

c) Angular Acceleration:- 

Rate of change of angular velocity with respect to time is Called 'Angular Acceleration'.

Linear Displacement, Velocity & Acceleration

a) Linear Displacement-

The total path traveled by an object from its initial position irrespective of the type of motion (i.e Straight or curved motion) is called as its 'linear displacement'. 

Linear displacement depends only on the movement of object and is independent of initial and final position of the object.If the initial and final positions of object are same, the linear displacement will not be considered as zero. Its linear displacement will be equal to the path traveled by that object before coming back to its initial position.

For  Example

b) Linear Velocity-

Rate of change of Linear displacement with respect to time is called 'Linear velocity'.

c) Linear Acceleration- 

Linear acceleration can be defined as the rate of change of linear velocity with respect to time. It is a vector quantity having magnitude and direction.

Negative acceleration is called as ‘Retardation’.

Formulas for Linear motion:-

i)   v - u = at

ii)   S = ut + 1/2at²

iii)   v² - u² = 2aS

Types of Motion

a) Plane Motion:-  When a body moves in a single plane. Its motion can be stated as 'Plane motion'.
Examples of Plane Motion-  
1)  The motion of Carrom board coins is plane motion as the coins move in a single plane on the plane face of Carrom board.
2)  The movement of vehicle on a plane ground.
3)  Rotation of ceiling fan as the blades rotate about center axis in a single plane.
4)  Rotation of planets around sun.

b) Rectilinear Motion:-  The motion along a straight single line is called 'Rectilinear motion'.
Examples of Rectilinear Motion-
1)  The motion of an object freely dropped from a height towards ground. Falling of fruits from trees good example of rectilinear motion.
2)  The motion of light is rectilinear motion.

c) Curvilinear Motion:-  The motion along a curved path but in a single plane is called 'Curvilinear motion.
Examples of Curvilinear Motion:-  
1)  The motion of ball hit by a cricket batsman or an object thrown at an angle from ground moves along a curvilinear motion.

Kinematics & Dynamics

The word 'Kinematics' is related to motion whereas the word 'Dynamics' relates to forces between machines parts.

Kinematics of machines explains the theory of relative motions of different parts of machines w.r.t. each another.
Dynamics of machines explains the forces between the various machine parts and their effects.