- Frame of Reference: Changing a person’s frame of reference (group standards or norms) can change attitudes, especially when new group norms are introduced (Asch, Newcomb, Lewin).
- Group Decision is Powerful: Group discussion and collective decision-making are more effective in changing attitudes than lectures.
- Lewin’s Food Habit Study: The Discussion Method (32%) was more effective than the Lecture Method (3%) in changing food habits during WWII.
- Reason for Effectiveness: Active participation and ego involvement in discussion create stronger and more lasting attitude change.
- Industrial Study (Lewin & Butler, 1953): Supervisors showed more improvement in reducing bias through discussion compared to lecture and control groups.
- Indian Study (Kothurkar, 1953): Emotional appeal showed more attitude change than rational and discussion methods, though results were not strongly significant.
Definitions [44]
Definition: Friction Force
The force which is exerted by a surface on a moving object or on an object making an effort to move, expressed as Ff = μ × FN where μ is the coefficient of friction, is called Friction Force.
Definition: Net Force
The vector sum of all forces acting on an object is called Net Force.
Definition: Spring Force
The force exerted by a compressed or stretched spring upon or by an object, expressed as Fspring = −kx (Hooke's Law), is called spring Force.
Definition: Tension Force
The force transmitted by a string, rope, or wire when pulled tightly by forces acting from its ends, whose magnitude is the same everywhere in the rope, is called tension Force.
Definition: Applied Force
The force which is applied to an object by a person or another object is called applied Force.
Definition: Gravity Force
The force of gravity on Earth which is always equal to the weight of the body, expressed as Fgrav = mg where g = 9.8 m/s2, is called Gravity Force.
Definition: Long Range (Non-contact) Force
The force which can act over distances without any physical contact between objects, such as Gravitational Force, Electrical Force, and Magnetic Force, is called Long Range or Non-contact Force.
Definition: Contact Force
The force which acts through direct physical contact between two objects, such as Frictional Force, Tensional Force, Normal Force, Air Resistance Force, Applied Force, and Spring Force, is called Contact Force.
Definition: Force
The push or pull which, when applied on an object, changes or tends to change (i) the state of rest, (ii) the state of uniform motion, or (iii) the shape and size of the object, measured in newton with dimension [MLT⁻²], is called Force.
Definition: Normal Force
The support force exerted perpendicularly by a surface on an object in contact with it is called the normal force.
Definition: Aristotle's Fallacy
Aristotle's statement: “An external force is required to keep a body in uniform motion”.
Definition: Inertia of Direction
The inability of a body to change its direction of motion by itself is called inertia of direction.
Definition: Inertia
The inability of a body to change its state of rest or of uniform motion or its direction by itself is called Inertia.
Definition: Inertia of Rest
The inability of a body to change its state of rest by itself is called inertia of rest.
Definition: Inertia of Motion
The inability of a body to change its state of uniform motion by itself is called inertia of motion.
Define Newton’s second law of motion.
Newton’s second law of motion states that the rate of change of momentum is directly proportional to force applied and takes place in the direction of the force.
Definition: Impulse of a Force
The quantity ‘change in momentum’ is separately named as the Impulse of the force.
OR
The quantity change in momentum is called impulse.
OR
Impulse
The product of a large force applied on a body for a very short interval of time, which produces a finite change in the momentum of the body, with SI unit Ns (or kg-ms⁻¹) and dimension [MLT⁻¹], is called impulse.
J = Ft = m(v − u) = change in momentum
Definition: Friction
The force which prevents or tries to prevent the slipping or sliding of two surfaces in contact, which can be high for dry and rough surfaces and low for smooth and wet surfaces, is called Friction.
Definition: Angle of Repose
The minimum angle of the rough inclined plane for which a body placed on it may just start sliding down, which is numerically equal to the angle of friction, is called the Angle of Repose.
Definition: Angle of Friction
The angle between the resultant force (combination of normal force and frictional force) and the normal force itself, related to the coefficient of friction as tan(ϕ) = μ, i.e., ϕ = tan−1(μ), is called the Angle of Friction.
Definition: Rolling Friction
"Friction between two bodies in contact when one body is rolling over the other, is called rolling friction."
OR
The resistive force or rolling resistance that occurs when an object rolls across a surface and slows down the motion of a rolling ball/wheel, which is the weakest form of friction compared to static/sliding friction, is called Rolling Friction.
Definition: Centrifugal Force
The non-real (fictitious) force directed along the radius away from the centre of a circle (opposite to centripetal acceleration) is called centrifugal force.
Define centripetal force.
The force acting on a particle performing uniform circular motion along the radius and directed towards the centre of the circle is called the centripetal force.
The mathematical form of centripetal force is:
F = `mv^2/r`
where:
F = centripetal force,
m = mass of the object,
v = speed or velocity, and
r = radius
Definition: Circular Motion
When a particle moves in two dimensions or in a plane such that its distance from a fixed (or moving) point remains constant, then its motion is called circular motion.
Definition: Uniform Circular Motion
The circular motion in which the speed of a particle is constant but its direction changes continuously, and acceleration is always directed towards the centre, is called uniform circular motion.
Definition: Centripetal Force
The force directed along the radius towards the centre of a circle, which is necessary to keep the object moving in a circle, is called centripetal force.
Definition: Kinetic Friction
Friction between two surfaces in contact when one body is actually sliding over the other body is called kinetic friction or dynamic friction.
OR
The force of friction that comes into play when a body is in a steady state of motion over another surface is called the force of kinetic friction.
OR
The resistive force that acts between moving surfaces that are in relative motion, always acting opposite to the direction of velocity and tending to slow down the speed of an object, expressed as Fk = μk × N, is called Kinetic Friction.
Definition: Static Friction
The frictional force that balances the applied force when the body is static (or at rest). It prevents sliding motion between two surfaces in contact.
OR
The friction that acts on an object when it is not in motion relative to the surface and acts in the direction to cancel out the applied force F, whose magnitude varies with the applied force up to a maximum limit fs,max = μs × N, is called Static Friction.
Definition: Inertial Frame of Reference
A frame where Newton's Laws of motion are applicable, which is either at rest or moving with uniform velocity relative to a fixed imaginary axis, where acceleration of a body is caused by real forces and equation of motion is ΣFreal = ma, is called an Inertial Frame of Reference.
Definition: Non-Inertial Frame of Reference
A frame where Newton's Laws are not applicable, which moves with either uniform or non-uniform acceleration, and where all accelerated and rotating frames fall under this category, is called a Non-Inertial Frame of Reference.
Definition: Frame of Reference
A coordinate system that defines the position of a particle or an event in space is called a frame of reference.
Definition: Frame of Reference
The reference with respect to which the position or motion of a particle is defined — consisting of the combination of a coordinate system and a clock — is called a frame of reference.
Definition: Centripetal Force
Centripetal force is the force acting on a body moving in a circular path, in a direction towards the centre of the circular path.
OR
A force acts on any object moving along a circle and it is directed towards the centre of the circle. This is called the Centripetal force.
OR
The inward force required to keep an object moving in a circular path, directed towards the centre of the circle, expressed as FC = \[\frac {mv^2}{r}\] = mrω2, which always acts perpendicular to the direction of linear velocity, is called Centripetal Force.
Define Centripetal force.
At each of circular path, the particle, instead of moving straight continuously, turn towards the centre. Therefore, the motion in the circular path is under the action of a force called the centripetal force.
Definition: Pseudo Force
A force which does not arise from any physical interaction but appears when observing motion from a non-inertial (accelerated) frame of reference, arising due to the acceleration of the observer's frame, is called a pseudo force.
Definition: Real Force
A force which arises due to physical interaction between objects is called a real force.
OR
Forces acting on an object due to interaction with another object, such as Normal force, Tension, Weight, Spring force, and Muscular force, which form action-reaction pairs and are all fundamental forces of nature, are called Real Forces.
Define angular velocity.
Angular velocity of a particle is the rate of change of angular displacement.
Define Uniform circular motion.
When a particle moves with a constant speed in a circular path, its motion is said to be the uniform circular motion.
Definition: Centripetal Force
The force directed towards the centre along the radius, required to keep a body moving along a circular path at constant speed, is called centripetal force.
Definition: Radial (Centripetal) Acceleration
The component of acceleration directed towards the centre of the circular path is called centripetal acceleration (or radial acceleration).
Definition: Angular Acceleration (α)
The rate of change of angular velocity of a body is called angular acceleration.
Definition: Angular Velocity (ω)
The rate of change of angular displacement of a body undergoing circular motion is called angular velocity.
Definition: Angular Displacement
The angle traced out by the radius vector at the centre of the circular path in a given time, expressed as Δθ = θ2 − θ1, is called angular displacement.
Definition: Uniform Circular Motion
When a particle moves with a constant speed in a circular path, its motion is said to be uniform circular motion.
OR
The motion of a body moving with constant speed along a circular path is called uniform circular motion.
OR
The motion of a body moving with constant speed along a circular path, where the velocity is always tangential to the circular path and remains constant in magnitude, is called uniform circular motion.
Formulae [13]
Formula: Tension Force
For two masses m₁ and m₂ connected by a string over a pulley:
-
Acceleration: a = \[\frac{(m_1-m_2)}{m_1+m_2}\] × g
-
Tension: T = \[\frac{2m_1m_2}{m_1+m_2}\] × g
Formula: Newton's First Law of Motion
\[\vec F\] = m \[\frac{d\vec{\mathrm{v}}}{dt}\] = m\[\vec a\] ... (for constant mass)
Thus, if \[\vec F\] = 0, \[\vec v\] is constant. Hence, if there is no force, velocity will not change. This is nothing but Newton's first law of motion.
Formula: Newton's Second Law of Motion
General Form: \[\vec F\] =\[\frac{d\vec{p}}{dt}\]
For Constant Mass: \[\vec F\] = m\[\vec a\]
Momentum: \[\vec p\] = m\[\vec v\]
Formula: Impulse
\[{\vec{\mathrm{J}}=\vec{\mathrm{F}}t}=\mathrm{m}(\vec{\mathrm{v}}-\vec{\mathrm{u}})\]
Formula: Newton's Third Law of Motion
\[\vec{F}=\frac{d\vec{p}}{dt}=\frac{d\left(m\vec{\mathrm{v}}\right)}{dt}\]
Formula: Centripetal Force
\[\vec{F}=-\frac{mv^2}{r}\hat{r}_0\]
Directed towards the centre (negative sign indicates inward direction).
Formula: Centrifugal Force
\[\vec{F}=+\frac{mv^2}{r}\hat{r}_0\]
Directed away from the centre (positive sign indicates outward direction).
Formula: Coefficient of Kinetic Friction
μₖ = Fₖ/N
The coefficient of kinetic friction is defined as the ratio of force of kinetic friction to the normal reaction between the two surfaces in contact.
Formula: Kinetic Friction
Fₖ = μₖ N
Where:
- Fₖ = Force of kinetic friction
- μₖ = Coefficient of kinetic friction (constant of proportionality)
- N = Normal reaction between the two surfaces in contact
Formula: Coefficient of Static Friction
μs = FL / N
Where:
- μs = Coefficient of static friction
- FL = Limiting force of friction
- N = Normal reaction
Formula: Static Friction
FL = μs N
Where:
- FL = Limiting force of friction (maximum static friction)
- μs = Coefficient of static friction (dimensionless constant)
- N = Normal reaction (normal force between surfaces)
Formula: Centripetal Force
\[F_C=\frac{mv^2}{r}=mr\omega^2=mv\omega\quad(v=r\omega)\]
Formula: Pseudo Forces
Pseudo Force: Fpseudo = −m\[\vec a\]
Where:
- m = mass of the object
- \[\vec a\] = acceleration of the non-inertial reference frame
- The negative sign indicates the force is opposite to the acceleration direction
Theorems and Laws [8]
Law: Law of Inertia
Statement: The law of inertia shows that a body will preserve its velocity and direction till no force in the direction of its motion acts upon it.
- A more massive object has more inertia.
- To maintain uniform motion along a straight line, balanced forces are required.
- Unbalanced external forces acting on a body can only bring a change in its state of motion.
Law: Newton's First Law of Motion
Statement:
Every inanimate object continues to be in a state of rest or of uniform unaccelerated motion along a straight line, unless it is acted upon by an external, unbalanced force.
Importance:
- It shows the equivalence between the state of rest and the state of uniform motion along a straight line — the distinction lies only in the choice of frame of reference.
- It defines force as a physical entity that brings about a change in the state of motion or rest of an object.
- It defines inertia as a fundamental and inherent property of every physical body by virtue of which it resists any change in its state of rest or uniform motion along a straight line.
Law: Newton’s Second Law of Motion
Statement:
The rate of change of linear momentum of a rigid body is directly proportional to the applied (external unbalanced) force and takes place in the direction of force.
F = Δp = m\[\frac {dv}{dt}\] = ma
Importance:
- It provides a mathematical formulation for the quantitative measure of force: F = \[\frac {Δp}{Δt}\] = ma.
- It defines momentum as the product of mass and velocity: p = mv.
- Aristotle's fallacy is overcome by establishing that it is the resultant unbalanced force — not force itself — that is required to maintain a change in the state of motion.
Law: Impulse-Momentum Theorem
Statement: The impulse of a force equals the change in momentum of the body.
J = Ft = m(v − u) = Δp
-
When a force acts from time t1 to t2:
\[\int_{t_1}^{t_2}Fdt=\int_{p_i}^{p_f}dp\]
- Impulse from a force-time graph = Area under the F-t graph.
- For constant force: J = Ft
Law: Newton's Third Law of Motion
Statement:
To every action (force) there is always an equal and opposite reaction (force).
Importance:
- It defines action and reaction as a pair of equal and opposite forces acting along the same line — whenever one object exerts a force on another, the second object exerts an equal and opposite force on the first.
- Action and reaction forces always act on different objects and therefore never cancel each other out.
Law: Conservation of Linear Momentum
Statement: The total momentum of a system of particles remains constant as long as no external forces act upon it.
m1\[\vec v_1\] + m2\[\vec v_2\] + … = constant
-
When no external forces act on colliding objects, the vector sum of linear momentum of each body remains constant and is not affected by mutual interaction.
Theorem: Lami's Theorem
Statement: When three forces F₁, F₂ and F₃ act on a body and are in equilibrium, each force is proportional to the sine of the angle between the other two forces.
Formula:
\[\frac {F_1}{sinα}\] = \[\frac {F_2}{sinβ}\] = \[\frac {F_3}{sinγ}\]
where α, β, and γ are the angles opposite to forces F₁, F₂, and F₃ respectively.
Law: Laws of Friction
- First Law: When two bodies are in contact with each other, the direction of the force of friction on one at its point of contact is opposite to the direction in which the point of contact tends to move relative to the other.
- Second Law: When bodies are in equilibrium, the force of friction prevents the motion, which can be determined by using conditions of equilibrium of forces that act on the body.
- Third Law: The ratio of limiting friction to the normal reaction of surfaces depends on the nature of the substances and does not depend on the magnitude of the normal reaction.
- Fourth Law: The amount of limiting friction is independent of the area of contact or the shape of surfaces, provided the normal reaction remains unchanged.
- Fifth Law: During motion, the direction of friction is opposite to that of relative motion and is independent of velocity.
Key Points
Key Points: Application of Conservation of Momentum(Rocket Propulsion)
Statement: The initial momentum of a rocket at its launching pad is zero. When fired, the exhaust gases rush downward at high speed. To conserve momentum, the rocket moves upwards.
Thrust on the rocket:
F = − v\[\frac {dm}{dt}\]
The negative sign indicates that the direction of thrust is opposite to the direction of escaping gases.
Acceleration of the rocket:
a = \[\frac {v}{m}\]\[\frac {dm}{dt}\]
where v = velocity of exhaust gases and \[\frac {dm}{dt}\] = rate of fuel consumption = rate of ejection of fuel.
Key Points: Frame of Reference
Key Points: Uniform Circular Motion
- In UCM, speed is constant, but velocity continuously changes direction, always remaining tangential to the path.
- Angular displacement is the angle swept by the radius vector; angular velocity is its rate of change.
- Even at constant speed, centripetal acceleration is never zero — it always acts towards the centre of the circular path.
- Centripetal force is always directed towards the centre and is essential to maintain circular motion — it does no work on the body.
- If speed is constant in circular motion, tangential acceleration = 0, but radial acceleration ≠ 0.
Concepts [20]
- Concept of Force
- Aristotle’s Fallacy
- The Law of Inertia
- Newton's First Law of Motion
- Newton’s Second Law of Motion
- Impulse of a Force
- Newton's Third Law of Motion
- Conservation of Momentum
- Equilibrium of a Particle
- Common Forces in Mechanics
- Friction
- Types of Friction>Rolling Friction
- Circular Motion and Its Characteristics
- Solving Problems in Mechanics
- Types of Friction>Kinetic Friction
- Types of Friction>Static Friction
- Frame of Reference
- Centripetal Force
- Types of Forces>Real and Pseudo Forces
- Uniform Circular Motion (UCM)
