- 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 [28]
Definition: Motion
A body that changes its position with time (always relative to the observer) is called a body in motion.
Definition: One-Dimensional Motion
The motion in which only one coordinate changes with time (e.g., motion of a car on a straight road, motion of a freely falling body) is called one-dimensional motion.
Definition: Two-Dimensional Motion
The motion in which two coordinates change with time (e.g., an insect crawling over the floor, motion of a car turning at a corner) is called two-dimensional motion.
Definition: Three-Dimensional Motion
The motion in which position changes in space with time with respect to a frame of reference (e.g., motion of a kite) is called three-dimensional motion or motion in space.
Definition: Uniform Motion
The motion in which a particle covers equal displacements in equal intervals of time — requiring no net force — where velocity is independent of choice of origin and time interval is called uniform motion.
Definition: Non-Uniform Motion
The motion in which an object covers unequal distances in equal intervals of time, or when a body travels equal distances in unequal intervals of time, is called non-uniform motion.
Definition: Uniformly Accelerated Motion
The motion in which the velocity of an object changes equally in every equal interval of time — shown by a horizontal line in the acceleration-time graph indicating constant acceleration at any moment — is called uniformly accelerated motion.
Definition: Rest
A body that does not change its position with time with respect to its surroundings is called a body at rest.
Definition: Point Mass Object (Particle)
An object whose size is negligible compared to its range of motion is called a point mass object or particle.
Definition: Distance
The total length of the actual path covered by a body in travelling from its initial to its final position — a scalar quantity that always depends on the path followed, can never be negative, and has SI unit metre (m) — is called distance.
Definition: Displacement
The shortest straight line distance between an object's initial and final positions, represented as Δ\[\vec x\] = \[\vec x_2\] − \[\vec x_1\], is called displacement.
OR
The shortest distance from the initial to the final position of a body undergoing motion — a vector quantity whose direction is always from initial to final position, which does not depend on path but only on initial and final positions, and may be positive, negative, or zero — is called displacement.
Definition: Average Velocity
"Average velocity is defined as the displacement of the object during the time interval over which average velocity is being calculated, divided by that time interval."
OR
The total displacement Δ\[\vec x\] of an object divided by the total time interval Δt over which that displacement occurs is called average velocity.
OR
The ratio of total displacement to the total time taken by the body is called average velocity.
Definition: Instantaneous Velocity
Instantaneous velocity of an object is its velocity at a given instant of time. It is defined as the limiting value of the average velocity of the object over a small time interval (Δt) around t when the value of the time interval (Δt) goes to zero.
OR
The limiting value of the average velocity of an object over a small time interval 'Δt' around time t when the value of the time interval goes to zero is called instantaneous velocity.
Definition: Non-Uniform Speed (Variable Speed)
The speed at which an object covers unequal distances in equal intervals of time is called non-uniform speed or variable speed.
Definition: Average Speed
"total path length travelled during the time interval over which average speed is being calculated, divided by that time interval."
OR
The total distance travelled by an object divided by the total time taken for its motion is called average speed.
OR
The ratio of total distance travelled by the body to the total time taken to cover such distance is called average speed.
Definition: Uniform Speed
The speed at which an object covers equal distances in equal intervals of time is called uniform speed.
Definition: Instantaneous Speed
Instantaneous speed is simply the speed of an object at a single, specific moment in time (t).
OR
The limiting value of the average speed of an object over a small time interval 'Δt' around time tt when the value of the time interval goes to zero is called instantaneous speed.
Definition: Retardation / Deceleration
The negative acceleration (i.e., uniformly retarded motion where a < 0) that shows slowing down or deceleration of a particle is called retardation.
Definition: Instantaneous Acceleration
The limiting value of the average acceleration of an object over a small time interval 'Δt' around time tt when the value of the time interval goes to zero is called instantaneous acceleration.
OR
The acceleration of a particle at a particular instant of time — defined as the limit of average acceleration as time interval Δt→0 — is called instantaneous acceleration.
Definition: Average Acceleration
The change in velocity of an object divided by the total time required for that change in velocity is called average acceleration.
OR
The ratio of total change in velocity to the total time taken by the particle when the change in velocity results is called average acceleration.
Definition: Gravitational Acceleration
The acceleration on an object which results due to gravity — where every small body accelerates in a gravitational field at a similar rate towards the centre of mass, irrespective of the mass of the body — is called gravitational acceleration.
Definition: Acceleration
Acceleration is defined as the rate of change of velocity with time.
OR
The rate of change of velocity with respect to time — a vector quantity whose direction is the same as that of change in velocity, with dimensional formula [M0L1T−2] and SI unit m/s² — is called acceleration.
Definition: Uniform Acceleration
The acceleration when the magnitude and direction of the acceleration remains constant during motion of an object is called uniform acceleration.
Definition: Non-Uniform Acceleration
The acceleration when either magnitude or direction or both change during motion is called non-uniform acceleration.
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: 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
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.
Formulae [9]
Formula: Displacement
If the position at time t₁ is x₁ and at time t₂ is x₂, then
Displacement \[\vec s\] = \[\vec x_2\] - \[\vec x_1\]
In vector form:
\[\Delta\bar{r}=(x_2-x_1)\hat{i}+(y_2-y_1)\hat{j}+(z_2-z_1)\hat{k}\]
Formula: Average Velocity
\[\vec{v}_{\mathrm{av}}=\frac{\vec{x}_2-\vec{x}_1}{t_2-t_1}\]
- vav : average velocity.
- x2 : final position vector.
- x1 : initial position vector.
- t2 : final time
- t1 : initial time
Dimensions: [L1M0T−1]
OR
Average Velocity: \[\vec V_{avg}\] = \[\frac {\text {Displacement}}{\text {Time interval}}\] = \[\frac {x_2-x_1}{t_2-t_1}\] = \[\frac {Δ\vec x}{Δt}\]
Formula: Velocity
Velocity = \[\frac {\text {Displacement}}{\text {Time interval}}\]
Formula: Instantaneous velocity
\[\vec{\mathrm{v}}=\lim_{\Delta t\to0}\left(\frac{\Delta\vec{x}}{\Delta t}\right)=\frac{d\vec{x}}{dt}\]
Formula: Speed
Speed = \[\frac {Distance covered}{t}\] = \[\frac {s}{t}\]
Formula: Average Speed
Average Speed = vav = \[\frac{\text{path length}}{\text{time interval}}\]
OR
Average speed = \[\frac {\text {Total path length}}{\text {Total time int erval}}\] = \[\frac {\text {Total distance}}{\text {Total time}}\] = \[\frac {x}{t}\]
Formula: Instantaneous Speed
To calculate instantaneous speed, we look at the average speed () over a very, very short time interval (Δt). It is defined as the limiting value of the average speed as the time interval (Δt) approaches zero.
Instantaneous Speed = \[\operatorname*{lim}_{\Delta t\to0}\frac{\mathrm{Distance}}{\Delta t}\]
OR
\[\vec{\mathbf{v}}=\lim_{\Delta t\to0}\frac{\Delta\vec{\mathbf{x}}}{\Delta t}=\frac{d\vec{\mathbf{x}}}{dt}\]
Formula: Instantaneous Acceleration
Instantaneous acceleration is the limiting value of average acceleration when the time interval approaches zero:
\[\vec{a}=\lim_{\Delta t\to0}\frac{\Delta\vec{v}}{\Delta t}=\frac{d\vec{v}}{dt}\]
where:
- \[\vec a\] = instantaneous acceleration
- \[d\vec{v}\] = infinitesimal change in velocity
- dt = infinitesimal change in time
The instantaneous acceleration at a given time equals the slope of the tangent to the velocity versus time curve at that time.
Formula: Average Acceleration
Average acceleration is calculated when an object has velocities \[\vec v_1\] and \[\vec v_2\] at times t1 and t2:
\[\vec{a}=\frac{\vec{v_2}-\vec{v_1}}{t_2-t_1}\]
where:
- \[\vec a\] = average acceleration
- \[\vec v_1\] = velocity at time t1
- \[\vec v_2\] = velocity at time t2
OR
Average acceleration: \[\vec a_{av}=\frac {\vec v_2-\vec v_1}{t_{2}-t_{1}}=\frac {\Delta\vec v}{\Delta t}\]
Key Points
Key Points: Frame of Reference
