Read & Learn Some Physics Formulas and Definitions In Simple Way Of Force and Motion Chapter
Learn Some Physics Formulas and Definitions In Simple Way Of Force and Motion Chapter
Chapter 1
Force And Motion
Topic - 1. Equation Of Motion
Force
Force is any influence that causes an object to undergo a certain change in its movement, direction, or geometrical construction.
A force has both magnitude and direction, making it a vector quantity.
Motion
Motion is a change in position of an object with respect to time and its reference point.
Motion is observed by attaching a frame of reference to a body and measuring its change in position relative to another reference frame.
An object's motion cannot change unless it is acted upon by a force, as described by Newton's first law.
Velocity
Velocity is the rate of change of the position (displacement) of an object, equivalent to a specification of its speed and direction of motion.
Speed describes only how fast an object is moving; whereas velocity gives both how fast and in what direction the object is moving.
A constant velocity means motion in a straight line (constant direction) at a constant speed.
Velocity is a vector physical quantity; both magnitude and direction are required to define it.
Acceleration
If there is a change in speed, direction, or both, then the object is said to have a changing velocity and is undergoing an acceleration.
The rate of change of velocity is "acceleration" (in m/s2), which describes how an object's speed and direction of travel change at each point in time.
Equation of motion
The average velocity of an object moving through a displacement, d during a time interval, t is
d / t
Average velocity magnitudes are always smaller than or equal to average speed of a given particle.
The final velocity v of an object which starts with velocity u and then accelerates at constant acceleration a for a period of time t is:
v = u + at
The average velocity of an object undergoing constant acceleration is
(u+v) / 2
where u is the initial velocity and v is the final velocity.
To find the position, x, of such an accelerating object during a time interval, t, then:
(u+v) t / 2
When only the object's initial velocity is known, the expression,
x = u t + ½at²
These basic equations for final velocity and position can be combined to form an equation that is independent of time, also known as Torricelli's equation:
v ² = u² + 2 a x
Relative velocity
Relative velocity is a measurement of velocity between two objects as determined in a single coordinate system
If an object A is moving with velocity vector v and an object B with velocity vector w, then the velocity of object A relative to object B is defined as the difference of the two velocity vectors:
V (A relative to B) = v – w
Similarly the relative velocity of object B moving with velocity w, relative to object A moving with velocity v is:
V (B relative to A) = w - v
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Topic - 2. Newton's Laws and Motion
Momentum
Linear momentum (SI unit kg m/s, or Ns) is a vector quantity, possessing a direction as well as a magnitude.
P = m v
Linear momentum is a conserved quantity, meaning that if a closed system is not affected by external forces, its total linear momentum cannot change. Conservation of linear momentum is implied by Newton's first law.
Newton's laws of motion
Newton's laws of motion are the basis for classical mechanics. They describe the relationship between the forces acting on a body and its motion due to those forces.
The First law is summarized as follows:
If there is no net force on an object, then its velocity is constant. The object is either at rest (if its velocity is equal to zero), or it moves with constant speed in a single direction.
The first law can be stated mathematically as
∑ F = 0 => dv / dt = 0
Consequently,
An object that is at rest will stay at rest unless an external force acts upon it.
An object that is in motion will not change its velocity unless an external force acts upon it.
Newton's second law:
The second law states that the net force on an object is equal to the rate of change (that is, the derivative) of its linear momentum p in an inertial reference frame:
F = dp / dt = d(mv) / dt
The second law can also be stated in terms of an object's acceleration. Thus,
F = m dv/dt = m a
where m is the mass of the body, and a is the body's acceleration.
Thus, the net force applied to a body produces a proportional acceleration. In other words, if a body is accelerating, then there is a force on it.
Impulse
An impulse J occurs when a force F acts over an interval of time Δt.
J = ∆p = m ∆v
Impulse is a concept frequently used in the analysis of collisions and impacts.
Newton's third law
The third law states that all forces exist in pairs: if one object A exerts a force FA on a second object B, then B simultaneously exerts a force FB on A, and the two forces are equal and opposite:
FA = −FB
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Topic -3. Newton's Law Of Universal Gravitation
Newton's law of universal gravitation
Newton's law of universal gravitation states that every point mass in the universe attracts every other point mass with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.
F= G m1 m2 / r2
where
F is the force between the masses,
G is the gravitational constant (universal gravitational constant, Newton's constant)
G is approximately equal to 6.674×10−11 N m2 kg−2
m1 is the first mass,
m2 is the second mass, and
r is the distance between the centers of the masses.
Weight
Weight of an object is the force on the object due to gravity.
It is the product of the mass m of the object and the magnitude of the local gravitational acceleration g ( 9.81m/sec² near the surface of the Earth)
W = m g
Weight and mass: Mass is an "extrinsic" property of matter, whereas weight is a force that results from the action of gravity on matter: it measures how strongly the force of gravity pulls on that matter.
The SI unit of weight is the same as that of force: the Newton (N) which can also be expressed as kg·m/s2
Density
The mass density or density of a material is its mass per unit volume.
P = m / V
Different materials usually have different densities. The mass density of a material varies with temperature and pressure.
The density of gases is strongly affected by pressure. The density of an ideal gas is
MP / RT
where M is the molar mass, P is the pressure, R is the universal gas constant (8.314 J K−1 mol−1 ) and T is the absolute temperature.
This means that the density of an ideal gas can be doubled by doubling the pressure, or by halving the absolute temperature.
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उत्तर प्रदेश के शहरों के व्हीकल यूनिक नंबर:-
Topic - 4 Circular Motion
Circular motion
Circular motion is a movement of an object along the circumference of a circle or rotation along a circular path. It can be uniform or non-uniform.
Since the object's velocity vector is constantly changing direction, the moving object is undergoing acceleration by a centripetal force in the direction of the center of rotation.
Uniform circular motion: It describes the motion of a body traversing a circular path at constant speed. The distance of the body from the axis of rotation remains constant at all times.
Formulas for uniform circular motion:
If the period for one rotation is T, the angular rate of rotation (angular velocity), ω is:
Ω = 2π / T
and the units are radians/sec
The speed of the object traveling the circle is:
v = 2 π r / T = ω r
The angle θ swept out in a time t is:
Θ = 2 π t / T = ω t
The acceleration due to change in the direction is:
a = v2 / r = ω2 r
Velocity
For a path of radius r, when an angle θ is swept out, the distance travelled on the periphery of the orbit is
s = r θ.
v = r dθ / dt = r ω
Acceleration
a= v dθ / dt = v ω = v2 / r
Torque
Torque is the tendency of a force to rotate an object about an axis.
Mathematically, torque is defined as the cross product of the lever-arm distance and force, which tends to produce rotation.
The magnitude of torque depends on three quantities: the force applied, the length of the lever arm connecting the axis to the point of force application, and the angle between the force vector and the lever arm.
T = r F sinθ
where
r is the length (or magnitude) of the lever arm vector,
F is the force vector
θ is the angle between the force vector and the lever arm vector.
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