Force
$\displaystyle \small \bullet$ Force is an external source/action which changes or tends to change the state of an object.
$\displaystyle \small \bullet$ It is a vector quantity i.e. it contains magnitude, direction and point of action.
$\displaystyle \small \bullet$ It is the product of mass of the object and the acceleration
$\displaystyle \small F=m\times a$
$\displaystyle \small \bullet$ Units of Force
$\displaystyle \small \circ$ MKS(SI): Newton (N), $\displaystyle \small kg-m/sec^{2}$
$\displaystyle \small \circ$ CGS: Dyne (D), $\displaystyle \small gm-cm/sec^{2}$
$\displaystyle \small \circ$ FPS: Poundal, $\displaystyle \small lb-ft/sec^{2}$
Types of Forces
1. Tensile force
When two equal and opposite forces having same line of action, act on an object, they tend to increase the length of the object.
The object is said to be under tension.
2. Compressive force
When two equal and opposite forces having same line of action, act on an object, they tend to decrease the length of the object.
The object is said to be under compression.
3. Shear force
When two equal and opposite forces having different line of action, act on an object, one section of object tends to slide over another section which results in shearing.
The object is said to be under shear.
Effects of Force
Tensile effect/Tension
Compressive effect/Compression
Shear effect/Shearing
Twisting effect
Bending effect
Breaking effect
Change in condition/state
Change in speed
Change in direction
Change in dimension
Resultant Force
Force acting in a straight line: direction of resultant force is same as greater force.
Parallel forces
Like Parallel forces
$\displaystyle \small R=P+Q$
$\displaystyle \small M\times PO=N\times OQ$
Unlike Parallel forces
$\displaystyle \small R=P+Q$
$\displaystyle \small M\times PO=N\times OQ$
Mutually intersecting forces
$\displaystyle \small \bullet$ When two or more forces act upon single point such that they form an angle with respect to each other, then their resultant force acts on the same point.
$\displaystyle \small \bullet$ This is calculated by Parallelogram Law of forces and Triangle Law of forces.
Composition of Forces
Parallelogram Law of Forces
$\displaystyle \small R=\sqrt{P^{2}+Q^{2}+2PQ\cos \theta }$
$\displaystyle \small \tan \alpha =\frac{Q\sin \theta }{P+Q\cos \theta }$
Triangle Law of Forces
$\displaystyle \small \frac{P}{AB}=\frac{Q}{BC}=\frac{R}{AC}$
Lami’s Theorem
$\displaystyle \small \frac{P}{\sin \theta }=\frac{Q}{\sin \alpha }=\frac{R}{\sin \beta }$
Resolution of Forces
$\displaystyle \small P=\frac{R\sin \beta }{\sin (\alpha +\beta )}$
$\displaystyle \small Q=\frac{R\sin \alpha }{\sin (\alpha +\beta )}$
Condition for Equilibrium of Forces Acting on a Body
$\displaystyle \small \bullet$ Sum of components of forces acting in the horizontal direction is equal to zero.
$\displaystyle \small \sum H=0$
$\displaystyle \small \bullet$ Sum of components of forces acting in the vertical direction is equal to zero.
$\displaystyle \small \sum V=0$
$\displaystyle \small \bullet$ Sum of moment acting at a point is zero.
$\displaystyle \small \sum M=0$
Linear Motion
Motion of an object in a straight line.
Ex: fruit falling from a tree
Circular Motion
Movement of an object on a circular path.
Ex: rotation of moon around the earth
Centrifugal Force
$\displaystyle \small \bullet$ When force is applied on an object rotating in a circular motion, it pushes the object away from the centre.
$\displaystyle \small \bullet$ Centrifugal force is calculated by,
$\displaystyle \small F=m\omega ^{2}r=\frac{mv^{2}}{r}$
$\displaystyle \small \bullet$ Its unit is Newton.
$\displaystyle \small \bullet$ It depends on the mass, rotational speed and distance of the object from the centre.
Centripetal Force
$\displaystyle \small \bullet$ When force is applied on an object rotating in a circular motion, it pulls the object towards the centre of the circular path.
$\displaystyle \small \bullet$ Centripetal force is calculated by,
$\displaystyle \small F=m\omega ^{2}r=\frac{mv^{2}}{r}$
$\displaystyle \small \bullet$ Magnitude of centripetal force = Magnitude of centrifugal force
Angular Displacement
$\displaystyle \small \bullet$ It is the angle subtended by an object moving on a circular path at the centre.
$\displaystyle \small \bullet$ Let A be the initial position of the object.
$\displaystyle \small \bullet$ After some time it moves to point B.
$\displaystyle \small \bullet$ The angle θ subtended after this movement at the centre is known an angular displacement.
$\displaystyle \small \bullet$ It is measure in radians or degrees.
Angular Velocity
$\displaystyle \small \bullet$ The rate of change of angular displacement is known as angular velocity.
$\displaystyle \small \bullet$ This is a vector quantity.
$\displaystyle \small \bullet$ SI unit is radian/second.
$\displaystyle \small \bullet$ It is denoted by $\displaystyle \small \omega$ (omega).
$\displaystyle \small \omega =\frac{\theta }{t}$
Angular Acceleration
$\displaystyle \small \bullet$ The rate of change of angular velocity is known as angular acceleration.
$\displaystyle \small \bullet$ SI unit is radian/second$\displaystyle \small ^{2}$
$\displaystyle \small \bullet$ It is denoted by α
$\displaystyle \small \alpha =\frac{d\omega }{dt}$
$\displaystyle \small \bullet$ Let the object rotates about a circular path of radius ‘r’
$\displaystyle \small \bullet$ This object completes one rotation in ‘t’ seconds
Angular velocity, $\displaystyle \small \omega =\frac{2\pi }{t}$
Linear velocity, $\displaystyle \small v =\frac{2\pi r}{t}$ [$\displaystyle \small v=\omega \times r$]
$\displaystyle \small \bullet$ Force is an external source/action which changes or tends to change the state of an object.
$\displaystyle \small \bullet$ It is a vector quantity i.e. it contains magnitude, direction and point of action.
$\displaystyle \small \bullet$ It is the product of mass of the object and the acceleration
$\displaystyle \small F=m\times a$
$\displaystyle \small \bullet$ Units of Force
$\displaystyle \small \circ$ MKS(SI): Newton (N), $\displaystyle \small kg-m/sec^{2}$
$\displaystyle \small \circ$ CGS: Dyne (D), $\displaystyle \small gm-cm/sec^{2}$
$\displaystyle \small \circ$ FPS: Poundal, $\displaystyle \small lb-ft/sec^{2}$
Types of Forces
When two equal and opposite forces having same line of action, act on an object, they tend to increase the length of the object.
The object is said to be under tension.
When two equal and opposite forces having same line of action, act on an object, they tend to decrease the length of the object.
The object is said to be under compression.
When two equal and opposite forces having different line of action, act on an object, one section of object tends to slide over another section which results in shearing.
The object is said to be under shear.
Effects of Force
Tensile effect/Tension
Compressive effect/Compression
Shear effect/Shearing
Twisting effect
Bending effect
Breaking effect
Change in condition/state
Change in speed
Change in direction
Change in dimension
Resultant Force
Force acting in a straight line: direction of resultant force is same as greater force.
Like Parallel forces
$\displaystyle \small M\times PO=N\times OQ$
Unlike Parallel forces
$\displaystyle \small M\times PO=N\times OQ$
Mutually intersecting forces
$\displaystyle \small \bullet$ When two or more forces act upon single point such that they form an angle with respect to each other, then their resultant force acts on the same point.
$\displaystyle \small \bullet$ This is calculated by Parallelogram Law of forces and Triangle Law of forces.
Composition of Forces
$\displaystyle \small \tan \alpha =\frac{Q\sin \theta }{P+Q\cos \theta }$
Triangle Law of Forces
Lami’s Theorem
Resolution of Forces
$\displaystyle \small Q=\frac{R\sin \alpha }{\sin (\alpha +\beta )}$
Condition for Equilibrium of Forces Acting on a Body
$\displaystyle \small \bullet$ Sum of components of forces acting in the horizontal direction is equal to zero.
$\displaystyle \small \sum H=0$
$\displaystyle \small \bullet$ Sum of components of forces acting in the vertical direction is equal to zero.
$\displaystyle \small \sum V=0$
$\displaystyle \small \bullet$ Sum of moment acting at a point is zero.
$\displaystyle \small \sum M=0$
Linear Motion
Motion of an object in a straight line.
Ex: fruit falling from a tree
Circular Motion
Movement of an object on a circular path.
Ex: rotation of moon around the earth
Centrifugal Force
$\displaystyle \small \bullet$ Centrifugal force is calculated by,
$\displaystyle \small F=m\omega ^{2}r=\frac{mv^{2}}{r}$
$\displaystyle \small \bullet$ Its unit is Newton.
$\displaystyle \small \bullet$ It depends on the mass, rotational speed and distance of the object from the centre.
Centripetal Force
$\displaystyle \small \bullet$ Centripetal force is calculated by,
$\displaystyle \small F=m\omega ^{2}r=\frac{mv^{2}}{r}$
$\displaystyle \small \bullet$ Magnitude of centripetal force = Magnitude of centrifugal force
Angular Displacement
$\displaystyle \small \bullet$ Let A be the initial position of the object.
$\displaystyle \small \bullet$ After some time it moves to point B.
$\displaystyle \small \bullet$ The angle θ subtended after this movement at the centre is known an angular displacement.
$\displaystyle \small \bullet$ It is measure in radians or degrees.
Angular Velocity
$\displaystyle \small \bullet$ The rate of change of angular displacement is known as angular velocity.
$\displaystyle \small \bullet$ This is a vector quantity.
$\displaystyle \small \bullet$ SI unit is radian/second.
$\displaystyle \small \bullet$ It is denoted by $\displaystyle \small \omega$ (omega).
$\displaystyle \small \omega =\frac{\theta }{t}$
Angular Acceleration
$\displaystyle \small \bullet$ The rate of change of angular velocity is known as angular acceleration.
$\displaystyle \small \bullet$ SI unit is radian/second$\displaystyle \small ^{2}$
$\displaystyle \small \bullet$ It is denoted by α
$\displaystyle \small \alpha =\frac{d\omega }{dt}$
$\displaystyle \small \bullet$ Let the object rotates about a circular path of radius ‘r’
$\displaystyle \small \bullet$ This object completes one rotation in ‘t’ seconds
Angular velocity, $\displaystyle \small \omega =\frac{2\pi }{t}$
Linear velocity, $\displaystyle \small v =\frac{2\pi r}{t}$ [$\displaystyle \small v=\omega \times r$]
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