Gravitational Acceleration
$\displaystyle \small \bullet$ The earth attracts every object towards itself thus generating acceleration in the object through its attraction.
$\displaystyle \small \bullet$ This acceleration due to gravity is called gravitational acceleration.
$\displaystyle \small \bullet$ It is denoted by ‘g’.
$\displaystyle \small \bullet$ Value and units:
$\displaystyle \small \circ$ M.K.S. system: 9.81 $\displaystyle \small m/sec^{2}$
$\displaystyle \small \circ$ C.G.S. system: 981 $\displaystyle \small cm/sec^{2}$
$\displaystyle \small \circ$ F.P.S. system: 32.2 $\displaystyle \small ft/sec^{2}$
Centre of Gravity (C.G.)
$\displaystyle \small \bullet$ Every object is made up of small particles.
$\displaystyle \small \bullet$ Due to gravitational force, each particle of an object is attracted towards earth.
$\displaystyle \small \bullet$ The resultant of all forces is known as weight and denoted by ‘W’.
$\displaystyle \small \bullet$ This weight is concentrated at a particular point of the object at which the object is in equilibrium.
$\displaystyle \small \bullet$ At this point object can be balanced at the tip of the needle. This point is known as centre of gravity.
$\displaystyle \small \bullet$ $\displaystyle \small \bar{x}$ and $\displaystyle \small \bar{y}$ are the coordinates of centre of gravity.
Centre of Gravity of Symmetrical Shapes
$\displaystyle \small \circ$ Centre of gravity of a circle is at its centre.
$\displaystyle \small \circ$ Centre of gravity of a semi circle is at $\displaystyle \frac{4r}{3\pi }$.
$\displaystyle \small \circ$ Centre of gravity of a sphere is at its centre.
$\displaystyle \small \circ$ Centre of gravity of a semisphere/hemisphere is at $\displaystyle \frac{3r}{8}$.
Conditions of Equilibrium
$\displaystyle \small \bullet$ An object is said to be in a state of equilibrium when all forces acting on it would not cause any displacement or rotation.
$\displaystyle \small \bullet$ Conditions to be in equilibrium
$\displaystyle \small \circ$ Algebraic sum of all horizontal components of forces acting on the object should be zero.
$\displaystyle \small \sum H=0$
$\displaystyle \small \circ$ Algebraic sum of all vertical components of forces acting on the object should be zero.
$\displaystyle \small \sum V=0$
$\displaystyle \small \circ$ Algebraic sum of all the moments on the object should be zero.
$\displaystyle \small \sum M=0$
Types of equilibrium
1. Stable equilibrium
A state of equilibrium in which a body tends to return to its original position after being displaced.
Ex: cone standing on its base.
2. Unstable equilibrium
A state of equilibrium in which a body does not return to its original position after being displaced.
Ex: cone standing on its top.
3. Neutral equilibrium
A state of equilibrium in which a body does not return to its original position after being displaced but new position is similar to the previous position.
Ex: base of cone placed on the inclined side.
$\displaystyle \small \bullet$ The earth attracts every object towards itself thus generating acceleration in the object through its attraction.
$\displaystyle \small \bullet$ This acceleration due to gravity is called gravitational acceleration.
$\displaystyle \small \bullet$ It is denoted by ‘g’.
$\displaystyle \small \bullet$ Value and units:
$\displaystyle \small \circ$ M.K.S. system: 9.81 $\displaystyle \small m/sec^{2}$
$\displaystyle \small \circ$ C.G.S. system: 981 $\displaystyle \small cm/sec^{2}$
$\displaystyle \small \circ$ F.P.S. system: 32.2 $\displaystyle \small ft/sec^{2}$
Centre of Gravity (C.G.)
$\displaystyle \small \bullet$ Due to gravitational force, each particle of an object is attracted towards earth.
$\displaystyle \small \bullet$ The resultant of all forces is known as weight and denoted by ‘W’.
$\displaystyle \small \bullet$ This weight is concentrated at a particular point of the object at which the object is in equilibrium.
$\displaystyle \small \bullet$ At this point object can be balanced at the tip of the needle. This point is known as centre of gravity.
$\displaystyle \small \bullet$ $\displaystyle \small \bar{x}$ and $\displaystyle \small \bar{y}$ are the coordinates of centre of gravity.
Centre of Gravity of Symmetrical Shapes
$\displaystyle \small \circ$ Centre of gravity of a circle is at its centre.
$\displaystyle \small \circ$ Centre of gravity of a semi circle is at $\displaystyle \frac{4r}{3\pi }$.
$\displaystyle \small \circ$ Centre of gravity of a sphere is at its centre.
$\displaystyle \small \circ$ Centre of gravity of a semisphere/hemisphere is at $\displaystyle \frac{3r}{8}$.
Conditions of Equilibrium
$\displaystyle \small \bullet$ An object is said to be in a state of equilibrium when all forces acting on it would not cause any displacement or rotation.
$\displaystyle \small \bullet$ Conditions to be in equilibrium
$\displaystyle \small \circ$ Algebraic sum of all horizontal components of forces acting on the object should be zero.
$\displaystyle \small \sum H=0$
$\displaystyle \small \circ$ Algebraic sum of all vertical components of forces acting on the object should be zero.
$\displaystyle \small \sum V=0$
$\displaystyle \small \circ$ Algebraic sum of all the moments on the object should be zero.
$\displaystyle \small \sum M=0$
Types of equilibrium
1. Stable equilibrium
A state of equilibrium in which a body tends to return to its original position after being displaced.
Ex: cone standing on its base.
A state of equilibrium in which a body does not return to its original position after being displaced.
Ex: cone standing on its top.
A state of equilibrium in which a body does not return to its original position after being displaced but new position is similar to the previous position.
Ex: base of cone placed on the inclined side.
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