## What is Thrust in Physics? | Definition, Example, Units – Hydrostatics

Thrust Physics Definition:
Total force acting perpendicular direction to the surface is called Thrust. The total normal force exerted by liquid at rest on a given surface is called thrust of liquid.

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## What is Thrust in Physics? | Definition, Example, Units – Hydrostatics

Example of Thrust in Daily Life:

• Thrust is to move forward as a crowd entering a stadium.
• Thrust is to force one’s self into a conversation.
• An example of thrust is a fish being expelled from the ocean by a strong wave.
• It is easy to carry or to walk with high heels, and cause thrust acting here (a perpendicular force).
• A pistole engine can produces thrust on its own.

Thrust Unit:
Thrust = Force
The SI unit of thrust is newton.
The CGS unit of thrust is dyne.

Hydrostatics:
Hydrostatics is a property of liquid or fluid in mechanics. A fluid is a material which flows at room temperature, because its upper molecule overlaps the inner molecule, which tends to flow the liquid in forward direction. In hydrostatics, we will learn about the condition of fluids when it is in rest or exerted by an external force. Here we will study the fluids in motion.

## Deforming Force in Physics | Definition, Examples, Types – Elasticity

Deforming Force Definition in Physics:
1. A force which produces a change in configuration of the object on applying it, is called a deforming force.

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## Deforming Force | Definition, Examples, Types – Elasticity

2. Firstly we take a body, Now we apply the external force to the body. After some time you see that the shape and the size of the body changes this property is known as Deforming Force.

Deforming Force Types:

• Elastic deformation is reversed when the force is removed.
• Inelastic deformation is not fully reversed when the force is removed – there is a permanent change in shape.
• Temporary deformation is also called elastic deformation, while the permanent deformation is called plastic deformation.

Deforming Force Examples:

• A pencil which is broken by applying force.
• Mild steel rods
• Iron rods

Elasticity:
Elasticity defines a property of an object that has the ability to regain its original shape after being stretched or compressed. Learn about the deforming force applied on an elastic object and how the stress and strain works on an object. What is a Hooke’s law and how it is applicable for the concept of elasticity.

## Uniform Motion and Non- Uniform Motion | Definition, Examples – Motion in a Straight Line

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Uniform Motion Definition:
If an object is moving along the straight line covers equal distance in equal interval of time, it is said to be in uniform motion along a straight line. Uniform Motion Example:

• A car moves at a constant speed on a straight path. At certain points travel time and traveled distance are measured and recorded.
• A vibrating spring in a sewing machine.

Non-Uniform Motion Definition:
This type of motion is defined as the motion of an object in which the object travels with varied speed and it does not cover same distance in equal time intervals, irrespective of the time interval duration. Non-Uniform Motion Example:

• Movement of an asteroid
• Dragging a box from a path

Motion in a Straight Line Topics:

## Adhesive Force in Physics | Meaning, Example – Surface Tension

The force of attraction acting between the molecules of different substances is called adhesive force.

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## Adhesive Force in Physics | Meaning, Example – Surface Tension

The force of attraction acting between the molecules of paper and ink, water and glass etc.

• Glass-Water
• Pen-Book
• Paint-Wall
• Marker-WhiteBoard

Surface Tension:
In Physics, the tension of the surface film of a liquid because of the attraction of the surface particles by the bulk of the liquid, which tries to minimize surface area is called surface tension. When the surface of the liquid is strong enough, then surface tension is applicable. It is strong enough to hold weight.

## Degrees of Freedom in Physics | Definition, Formula – Kinetic Theory of Gases

Degrees of Freedom in Physics Definition:
The degree of freedom for a dynamic system is the number of directions in which a particle can move freely or the total number of coordinates required to describe completely the position and configuration of the system.
It is denoted by f or N.

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## Degrees of Freedom in Physics | Definition, Formula – Kinetic Theory of Gases

Degrees of Freedom Formula Physics:
Suppose if we have A number of gas molecules in the container, then the total number of degrees of freedom is f = 3A. But, if the system has R number of constraints (restrictions in motion) then the degrees of freedom decreases and it is equal to f = 3A-R where A is the number of particles.
Degree of freedom of a system is given by

f or N = 3A – R

where,
A = number of particles in the system and
R = number of independent relations between the particles.

Degree of freedom for different atomic particles are given below.

1. For monoatomic gas = 3 (all translational).
2. For diatomic gas = 5 (3 translational, 2 rotational)
3. For non-linear triatomic gas = 6 (3 translational, 3 rotational)
4. For linear triatomic gas = 7 (3 translational,3 rotational and 1 vibrational)

Specific heat of a gas

(a) At constant volume, Cv = $$\frac{f}{2}$$R.
(b) At constant pressure, Cp = $$\left(\frac{f}{2}+1\right)$$R
(c) Ratio of specific heats of a gas at constant pressure and at constant volume is given by γ = 1 + $$\frac{2}{f}$$

Specific heat of solids, C = 3R ⇒ C = 24.93 Jmol-1 K-1.
Specific heat of water, C = 9R ⇒ C = 74.97 Jmol-1 K-1. Maxwell’s Law or the Distribution of Molecular Speeds
It derives an equation giving the distribution of molecules at different speeds

dN = 4πN$$\left(\frac{m}{2 \pi k T}\right)^{3 / 2} v^{2} e^{-\left(\frac{m v^{2}}{2 k T}\right)} \cdot d v$$

where, dN is number of molecules with speed between v and v + dv.
The $$\frac{d N}{d v}$$ versus v curve is shown below ### Law of Equipartition of Energy

This law states that, for a dynamic system in thermal equilibrium, the total energy is distributed equally amongst all the degree of freedom and the energy associated with each molecule per degree of freedom is

$$\frac{1}{2}$$ kB T.

where,
kB = 1.38 x 10-23 JK-1 is Boltzmann constant and
T is the absolute temperature of system on the kelvin scale.

Kinetic Theory of Gases:
In this concept, it is assumed that the molecules of gas are very minute with respect to their distances from each other. The molecules in gases are in constant, random motion and frequently collide with each other and with the walls of any container.

In this portion, you will learn about the properties of gases, based on density, pressure, temperature and energy. Continue reading here to learn more.

## Capillarity in Physics | Definition, Formula, Examples – Surface Tension

Capillarity Definition Physics:
The phenomenon of rise or fall of liquid column in a capillary tube is called capillarity.

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## Capillarity in Physics | Definition, Formula, Examples – Surface Tension

Ascent of a liquid column in a capillary tube is given by

h = $$\frac{2 S \cos \theta}{r \rho g}-\frac{r}{3}$$

Capillarity Formula Derivation:
If capillary is very narrow, then

h = $$\frac{2 S \cos \theta}{r \rho g}$$

where,
r = radius of capillary tube,
ρ = density of the liquid,
θ = angle of contact and
S = surface tension of liquid.

• If θ < 90°, cos θ is positive, so h is positive, i.e. liquid rises in a capillary tube.
• If θ > 90°, cos θ is negative, so h is negative, i.e. liquid falls in a capillary tube.
• Rise of liquid in a capillary tube does not violate law of conservation of energy.

Capillarity Examples in Daily Life:
(i) The kerosene oil in a lantern and the melted wax in a candle, rise in the capillaries formed in the cotton wick and burns.

(ii) Coffee powder is easily soluble in water because water immediately wets the fine granules of coffee by the action of capillarity.

(iii) The water given to the fields rises in the innumerable capillaries formed in the stems of plants and trees and reaches the leaves.

(iv) The tip of nib of a pen is split to provide capillary action for the ink to rise.

(v) The action of a towel in soaking up moisture from the body is due to the capillary action of cotton in the towel.

Surface Tension:
In Physics, the tension of the surface film of a liquid because of the attraction of the surface particles by the bulk of the liquid, which tries to minimize surface area is called surface tension. When the surface of the liquid is strong enough, then surface tension is applicable. It is strong enough to hold weight.

## Pressure Exerted by the Liquid – Hydrostatics

Pressure Exerted by the Liquid:
The normal force exerted by a liquid per unit area of the surface in contact is called pressure of liquid or hydrostatic pressure.

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## Pressure Exerted by the Liquid – Hydrostatics

Pressure exerted by a liquid column, p = hρg
where,
h = height of liquid column,
ρ = density of liquid
g = acceleration due to gravity.
Mean pressure on the walls of a vessel containing liquid upto height h is $$\left(\frac{h ρ g}{2}\right)$$.

Variation of Pressure with Depth:
Consider a fluid at rest having density ρ (roh) contained in a cylindrical vessel as shown in figure. Let the two points A and B separated by a vertical distance h. The pressure p at depth below the surface of a liquid open is given by
Pressure, p = pa + hpg
where,
ρ = density of liquid and
g = acceleration due to gravity.

Atmospheric Pressure:
The pressure exerted by the atmosphere on earth is called atmospheric pressure.

• It is equivalent to a weight of 10 tones on 1 m².
• At sea level, atmospheric pressure is equal to 76 cm of mercury column.

Then, atmospheric pressure

= hdg = 76 x 13.6 x 980 dyne/cm²
= 0.76 x 13.6 x 103 x 9.8 N/m²

Thus, 1 atm = 1.013 x 105 Nm-2 (or Pa)

The atmospheric pressure does not crush our body because the pressure of the blood flowing through our circulatory system is balanced by this pressure.

Atmospheric pressure is also measured in torr and bar.

1 torr = 1 mm of mercury column
1 bar = 105 Pa

• Aneroid barometer is used to measure atmospheric pressure.
• Pressure measuring devices are open tube manometer, tyre pressure gauge, sphygmomanometer etc.

Gauge Pressure:
Gauge pressure at a point in a fluid is the difference of total pressure at that point and atmospheric pressure. The liquid pressure at a point is independent of the quantity of liquid but depends upon the depth of point below the liquid surface. This is known as hydrostatic paradox.

### Important Points Related with Fluid Pressure

Important points related with fluid pressure are given below
(i) At a point in the liquid column, the pressure applied on it is same in all directions.

(ii) In a liquid, pressure will be same at all points at the same level.

(iii) The pressure exerted by a liquid depends only on the height of fluid column and is independent of the shape of the containing vessel. If hA = hB = hC, then pA = pB = pC

(iv) Consider following shapes of vessels Pressure at the base of each vessel
Px = Py = Pz = P0 + ρgh but wx ≠ wy ≠ wz
where,
ρ = density of liquid in each vessel,
h = height of liquid in each vessel and
p0 = atmospheric pressure.

(v) In the figure, a block of mass ‘m’ floats over a fluid surface If ρ = density of the liquid
A = area of the block
Pressure at the base of the vessel in p = p0 + ρgh + $$\frac{m g}{A}$$

Hydrostatics:
Hydrostatics is a property of liquid or fluid in mechanics. A fluid is a material which flows at room temperature, because its upper molecule overlaps the inner molecule, which tends to flow the liquid in forward direction. In hydrostatics, we will learn about the condition of fluids when it is in rest or exerted by an external force. Here we will study the fluids in motion.

## Velocity in Physics | Definition, Types, Formulas, Units – Motion in a Straight Line

Velocity Definition Physics
The time rate of change of displacement of an object in a particular direction is called its velocity.
Velocity Formula in Physics

$$Velocity =\frac{\text { Displacement }}{\text { Time taken }}$$

• Its SI unit is m/s.
• Its dimensional formula is [M°LT-1].
• It is a vector quantity, as it has both, the magnitude and direction.
• The velocity of an object can be positive, zero or negative.

## Velocity | Definition, Type, Formulas, Units – Motion in a Straight Line

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Types of Velocity in Physics

Uniform Velocity Definition:
If an object undergoes equal displacements in equal intervals of time, then it is said to be moving with a uniform velocity. Non-uniform Definition or Variable Velocity:
If an object undergoes unequal displacements in equal intervals of time, then it is said to be moving with a non-uniform or variable velocity. Average Velocity Definition:
The ratio of the total displacement to the total time taken is called average velocity.
Average Velocity Formula Physics

$$Average velocity =\frac{\text { Total displacement }}{\text { Total time taken }}$$

Instantaneous Velocity Definition:
The velocity of a particle at any instant of time is known as instantaneous velocity.
Instantaneous Velocity Formula

$$\text { Instantaneous velocity }=\lim _{\Delta t \rightarrow 0} \frac{\Delta x}{\Delta t}=\frac{d x}{d t}$$

Relative Velocity Definition:
Relative velocity of one object with respect to another object is the time rate of change of relative position of one object with respect to another object.

Relative velocity of object A with respect to object B
VAB =VA – VB
If it is in one dimensional motion, we can treat vectors as scalars just by assigning the positive sign to one direction and negative to others.

when two objects are moving in the same direction, then
VAB = VA – VB
or
VAB = VA – VB When two objects are moving in opposite direction, then
VAB = VA + VB
or
VAB = VA + VB When two objects are moving at an angle θ, then $$v_{A B}=\sqrt{v_{A}^{2}+v_{B}^{2}-2 v_{A} v_{B} \cos \theta}$$
and
$$\tan \beta=\frac{v_{B} \sin \theta}{v_{A}-v_{B} \cos \theta}$$

Motion in a Straight Line Topics:

## Rigid Body in Physics | Definition, Example, Types – Rotational Motion

Rigid Body Definition:
A body is said to be a rigid body, when it has perfectly definite shape and size. The distance between all points of particles of such a body do not change, while applying any force on it.

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## Rigid Body in Physics | Definition, Example, Types – Rotational Motion

The general motion of a rigid body consists of both

• Translational Motion
• Rotational motion Translational Motion in Physics:
Translational Motion of a rigid body performs a pure translational motion, if each particle of the body undergoes the same displacement in the same direction in a given interval of time. Rotational Motion Physics:
Rotational Motion of a rigid body performs a pure rotational motion, if each particle of the body moves in a circle, and the centre of all the circles lie on a straight line called the axes of rotation.

Equations of Rotational Motion:
(i) ω = ω0 + αt
(ii) θ = ω0t + $$\frac{1}{2}$$αt²
(iii) ω² = ω²0 + 2αθ

Rigid Body Example in Physics:
A ball bearing made of hardened steel is a good example of a rigid body. Now, drop a ball bearing on a polished marble floor — it’ll bounce just about as well as a Superball. Why’s that? Because, though it is a rigid body, it has near-perfect elasticity.

Rotational Motion:
In this portion, we will learn about the rotational motion of the objects. A body moves completely in rotational motion when each particle of the body moves in a circle about a single line. When a force is applied on a body about an axis it causes a rotational motion. The force applied here is called the torque. The axis of the rotation usually goes through the body. Also, learn the two theorems such as parallel axes and perpendicular theorem explained with respect to rotational motion of objects.

## Motion in a Plane | Definition, Formulas, Types – Motion in a Plane (Projectile and Circular Motion)

Motion in a Plane Physics:
Motion in plane is called as motion in two dimensions, e.g. projectile motion, circular motion. For the analysis of such motion our reference will be made of an origin and two co-ordinate axes X and Y.

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## Motion in a Plane | Definition, Formulas, Types – Motion in a Plane (Projectile and Circular Motion)

Terms Related to Motion in Plane
Few terms related to motion in plane are given below

1. Position Vector Definition:
A vector that extends from a reference point to the point at which particle is located is called position vector. Position vector is given by r = $$\hat{x} \hat{\mathbf{i}}+y \hat{\mathbf{j}}$$
Direction of this position vector r is given by the angle θ with X-axis,
where, tan θ = $$\frac{y}{x}$$
In three dimensions, the position vector is represented as
$$\mathbf{r}=x \hat{\mathbf{i}}+y \hat{\mathbf{j}}+z \hat{\mathbf{k}}$$ 2. Displacement Vector Definition:
The displacement vector is a vector which gives the position of a point with reference to a point other than the origin of the co-ordinate system. Magnitude of displacement vector
\begin{aligned} |\Delta \mathbf{r}| &=\sqrt{(\Delta x)^{2}+(\Delta y)^{2}} \\ &=\sqrt{\left(x_{2}-x_{1}\right)^{2}+\left(y_{2}-y_{1}\right)^{2}} \end{aligned}

Direction of the displacement vector Ar is given by
tan θ = $$\frac{\Delta y}{\Delta x}$$

In three dimensions, the displacement can be represented as
$$\Delta \mathbf{r}=\left(x_{2}-x_{1}\right) \hat{\mathbf{i}}+\left(y_{2}-y_{1}\right) \hat{\mathbf{j}}+\left(z_{2}-z_{1}\right) \hat{\mathbf{k}}$$ 3. Velocity Vector Definition:
Velocity of an object in motion is defined as the ratio of displacement and the corresponding time interval taken by the object.
(i) Average Velocity Definition:
It is defined as the ratio of the displacement and the corresponding time interval. Average velocity, $$v_{\mathrm{av}}=\frac{\Delta r}{\Delta t}=\frac{r_{2}-r_{1}}{t_{2}-t_{1}}$$
Average velocity can be expressed in the component forms as
$$v_{\mathrm{av}}=\frac{\Delta x}{\Delta t} \hat{\mathbf{i}}+\frac{\Delta y}{\Delta t} \hat{\mathbf{j}}=\Delta v_{x} \hat{\mathbf{i}}+\Delta v_{y} \hat{\mathbf{j}}$$

The magnitude of uav is given by
tan θ = $$\frac{\Delta v_{y}}{\Delta v_{x}}$$

(ii) Instantaneous Velocity Definition:
The velocity at an instant of time (t) is known as instantaneous velocity.
Instantaneous velocity, Magnitude of instantaneous velocity
$$|v|=\sqrt{v_{x}^{2}+v_{y}^{2}}$$
Direction of v is given by
tan θ = $$\left(\frac{v_{y}}{v_{x}}\right)$$

4. Acceleration Vector:
It is defined as the rate of change of velocity.
(i) Average Acceleration Definition:
It is defined as the change in velocity (Δv) divided by the corresponding time interval (Δt). Average acceleration, Magnitude of average acceleration is given by
$$\left|a_{\mathrm{av}}\right|=\sqrt{\left(a_{(\mathrm{av})} x\right)^{2}+\left(a_{(\mathrm{av})} y^{2}\right)^{2}}$$
Angle θ made by average acceleration with X-axis is
tan θ = $$\frac{a_{y}}{a_{x}}$$

(ii) Instantaneous Acceleration Definition:
It is defined as the limiting value of the average acceleration as the time interval approaches to zero.
Instantaneous acceleration,
a = $$\lim _{\Delta t \rightarrow 0} \frac{d v}{d t}$$
a = $$a_{x} \hat{\mathbf{i}}+a_{y} \hat{\mathbf{j}}$$
If acceleration a makes an angle θ with X-axis
then,
tan θ = $$\left(\frac{a_{y}}{a_{x}}\right)$$

Motion in Plane with Uniform Acceleration
A body is said to be moving with uniform acceleration, if its velocity vector suffers the same change in the same interval of time however small.
According to definition of average acceleration, we have
$$a=\frac{v-v_{0}}{t-0}=\frac{v-v_{0}}{t}$$
v = v0 + at
In terms of rectangular component, we can express it as
vx = v0x + axt
and
vy = v0y + ayt

Path of Particle Under Constant Acceleration
Now, we can also find the position vector (r). Let r0 and r be the position vectors of the particle at time t = 0 and t = t and their velocities at these instants be v0 and v respectively. Then, the average velocity is given by
$$\mathbf{v}_{\mathrm{av}}=\frac{\mathbf{v}_{0}+\mathbf{v}}{2}$$
Displacement is the product of average velocity and time interval. It is expressed as In terms of rectangular components, we have
$$x \hat{\mathbf{i}}+y \hat{\mathbf{j}}=x_{0} \hat{\mathbf{i}}+y \hat{\mathbf{j}}+\left(v_{0 x} \hat{\mathbf{i}}+v_{0, j} \hat{\mathbf{j}}\right) t+\frac{1}{2}\left(a_{x} \hat{\mathbf{i}}+a_{y} \hat{\mathbf{j}}\right) t^{2}$$

Now, equating the coefficients of $$\hat{\mathbf{i}} \text { and } \hat{\mathbf{j}},$$
x = x0 + v0xt + $$\frac{1}{2}$$axt² ……………. along x-axis
and
y = y0 + v0yt + $$\frac{1}{2}$$ayt² ……………. along y-axis

Note: Motion in a plane (two-dimensional motion) can be treated as two separate simultaneous one-dimensional motions with constant acceleration along two perpendicular directions.

Motion in a Plane (Projectile and Circular Motion):
In this chapter or under this topic, we are going to come across the motion of the object when it is thrown from one end to another end. This practice is said to be projection. Also, when an object is moved in a circular motion, then the equation of the motion is derived here. We will learn here about centripetal force and centripetal acceleration in detail with formulas. Also learn the force applied in everyday life motion of the particle in a vertical circle.