Long Notes – Motion – Class 9 – Science -Physics

Chapter 7– Motion

Long Notes – Motion – Class 9 – Science -Physics

7.1 Describing Motion

Describing Location:

◆Location of an object is described by specifying a reference point.

◆Example: School is 2 km north of the railway station. Railway station serves as the reference point.

Reference Point:

◆Reference point is a fixed location used to describe the position of an object.

◆In the example, railway station serves as the reference point for describing the location of the school.

Choice of Reference Point:

◆Reference point can be chosen based on convenience.

◆Different reference points can be used to describe the position of an object.

Origin:

◆Origin is the reference point used to describe the position of an object.

◆It serves as the starting point for measuring distances or locations.

Importance of Origin:

◆Origin helps in standardizing the description of positions.

◆It provides a common starting point for measurements and comparisons.

Versatility of Reference Points:

◆Reference points can vary based on the context or situation.

◆Different observers may choose different reference points depending on their perspective or requirements.

Consistency in Description:

◆Consistent use of reference points ensures clear and accurate communication of positions.

◆Using a standard origin helps in maintaining consistency across observations.

Flexibility in Selection:

◆Choice of origin can be flexible and may vary depending on the specific needs of the observer.

◆It allows for adaptability in describing positions in different scenarios.

7.1.1 MOTION ALONG A STRAIGHT LINE

Simplest Type of Motion:

◆Motion along a straight line is the simplest type of motion.

◆It involves an object moving along a straight path without deviation.

Example of Motion Along a Straight Line:

◆Consider an object moving along a straight path with reference point O.

◆Positions of the object at different instants are represented by points A, B, and C.

Calculation of Distance Covered:

◆The total path length covered by the object is the sum of distances OA and AC.

◆Distance is described by specifying only the numerical value, not the direction of motion.

Magnitude of Physical Quantity:

◆The numerical value of a physical quantity is its magnitude.

◆In this example, the magnitude of displacement is the shortest distance from O to C through A.

Difference between Distance and Displacement:

◆Distance traveled by an object is the actual path length covered.

◆Displacement is the shortest distance between initial and final positions, irrespective of the path taken.

Comparison between Distance and Displacement:

◆In the example, the distance traveled during motion from O to A and back to B is 85 km.

◆The magnitude of displacement is 35 km, which is not equal to the path length.

Possibility of Zero Displacement:

◆Displacement can be zero when the final position coincides with the initial position.

◆In this case, distance covered may still be nonzero if the object travels a round trip.

Distinction between Distance and Displacement:

◆Distance and displacement are two different physical quantities used to describe motion.

◆Distance accounts for the entire path length, while displacement focuses on the straight-line distance between initial and final positions.

7.1.2 UNIFORM MOTION AND NONUNIFORM MOTION

Uniform Motion:

◆In uniform motion, an object covers equal distances in equal intervals of time.

◆Example: If an object travels 5 m in the first second, 5 m more in the next second, and so on, it is in uniform motion.

Characteristics of Uniform Motion:

◆Equal distances covered in equal time intervals.

◆Speed remains constant throughout the motion.

Example of Uniform Motion:

◆Object covers 5 m in each second, demonstrating uniformity in motion.

◆Occurs when there is no acceleration or deceleration.

Time Interval in Uniform Motion:

◆Time intervals for uniform motion should be small to ensure consistency in distance covered.

Nonuniform Motion:

◆In nonuniform motion, objects cover unequal distances in equal intervals of time.

◆Example: A car moving on a crowded street or a person jogging in a park.

Characteristics of Nonuniform Motion:

◆Unequal distances covered in equal time intervals.

◆Speed may vary throughout the motion.

Examples of Nonuniform Motion:

◆Common in daily life situations where factors like traffic or terrain affect the speed of moving objects.

◆Varied speeds result in nonuniformity of motion.

Comparison between Uniform and Nonuniform Motion:

◆Uniform motion: Consistent speed and equal distances covered in equal time intervals.

◆Nonuniform motion: Varying speed and unequal distances covered in equal time intervals

7.2 Measuring the Rate of Motion

Rate of Motion and Speed:

◆Rate of motion refers to how quickly objects move.

◆Speed is a measure of the rate of motion, indicating the distance traveled by an object in a unit of time.

Measurement of Speed:

◆Speed is measured in units such as meters per second (m/s), centimeters per second (cm/s), or kilometers per hour (km/h).

◆The SI unit of speed is meters per second (m/s).

Description of Speed:

◆Speed is described by its magnitude, indicating how fast an object is moving regardless of direction.

Variability of Speed:

◆Speed of an object may vary over time, especially in non-uniform motion.

◆Average speed is used to describe the overall rate of motion, calculated by dividing total distance travelled by total time taken.

Average Speed Formula:

Average speed = Total distance travelled / Total time taken

Calculation of Speed:

Speed of an object can be calculated by dividing the distance travelled by the time taken.

Formula: Speed (v) = Distance (s) / Time (t)

7.2.1 SPEED WITH DIRECTION

Speed with Direction:

◆To provide a more comprehensive description of an object’s motion, both its speed and direction need to be specified.

◆The quantity that combines speed and direction is called velocity.

Definition of Velocity:

◆Velocity is the speed of an object moving in a specific direction.

◆It indicates both the magnitude of the speed and the direction of motion.

Characteristics of Velocity:

◆Velocity can be uniform or variable, depending on whether the speed or direction of motion changes.

◆Changes in velocity can occur by altering the object’s speed, direction, or both.

Calculation of Average Velocity:

◆Average velocity is calculated similarly to average speed, but it considers both speed and direction.

◆If an object is moving along a straight line at a variable speed, its average velocity is calculated as the total displacement divided by the total time taken.

Formula for Average Velocity (Uniform Motion):

◆In the case of uniform acceleration or deceleration, average velocity is the arithmetic mean of initial and final velocities.

◆Mathematically, average velocity (vav) = (initial velocity + final velocity) / 2.

Units of Speed and Velocity:

◆Speed and velocity share the same units, such as meters per second (m/s) or meters per second squared (m/s^2).

Example of Units:

Both speed and velocity are commonly expressed in meters per second (m/s) in the International System of Units (SI).

7.3 Rate of Change of Velocity

Uniform Motion:

◆In uniform motion along a straight line, velocity remains constant over time.

◆The change in velocity of the object during any time interval is zero.

Non-uniform Motion:

◆In non-uniform motion, velocity varies with time, having different values at different instants and points of the path.

◆The change in velocity of the object during any time interval is not zero.

Introduction of Acceleration:

◆Acceleration is a physical quantity that measures the change in velocity of an object per unit time.

◆It indicates how quickly the velocity of an object changes.

Formula for Acceleration:

Acceleration (a) = Change in velocity / Time taken.

If the velocity changes from an initial value (u) to a final value (v) in time (t), then acceleration (a) = (v – u) / t.

Types of Motion:

◆Accelerated Motion: Motion in which velocity changes, resulting in acceleration.

◆Uniformly Accelerated Motion: When an object’s velocity changes by equal amounts in equal intervals of time.

◆Non-uniform Accelerated Motion: When an object’s velocity changes at a non-uniform rate.

Direction of Acceleration:

◆Acceleration is positive if it’s in the direction of velocity and negative if it’s opposite to the direction of velocity.

Unit of Acceleration:

◆The SI unit of acceleration is meters per second squared (m/s^2), indicating the change in velocity per second.

7.4 Graphical Representation of Motion

Purpose of Graphs:

◆Graphs provide a convenient way to present information about various events or phenomena.

◆They help in visualizing patterns, trends, and relationships between different variables.

Example: Cricket Match Telecast:

◆In the telecast of a one-day cricket match, vertical bar graphs are often used to show the run rate of a team in each over.

◆These graphs help viewers understand the team’s performance over time.

Graphs in Mathematics:

◆In mathematics, straight line graphs are commonly used to represent linear equations with two variables.

◆They aid in solving equations and understanding the relationship between variables.

Graphs in Describing Motion:

◆To describe the motion of an object, line graphs are used.

◆Line graphs depict the dependence of one physical quantity, such as distance or velocity, on another quantity, such as time.

Dependent and Independent Variables:

◆In motion graphs, time is often considered as the independent variable, plotted on the x-axis.

◆The dependent variable, such as distance or velocity, is plotted on the y-axis.

Interpretation of Motion Graphs:

◆Motion graphs provide visual representations of an object’s motion over time.

◆They help in analyzing the object’s speed, acceleration, and displacement.

Utility of Line Graphs:

◆Line graphs are effective in illustrating trends, changes, and relationships between different variables related to motion.

◆They facilitate a clearer understanding of the behaviour of objects in motion.

7.4.1 DISTANCE–TIME GRAPHS

Representation of Motion:

◆Distance-time graphs represent the change in the position of an object over time.

◆Time is plotted along the x-axis, while distance is plotted along the y-axis.

Uniform Speed:

◆When an object travels equal distances in equal intervals of time, it moves with uniform speed.

◆In a distance-time graph for uniform speed, the distance traveled is directly proportional to the time taken.

◆This results in a straight line on the graph.

Determining Speed:

◆The speed of an object can be determined from a distance-time graph.

◆By considering a small part of the graph (e.g., from point A to point B), the speed can be calculated as the ratio of the change in distance to the change in time.

Acceleration:

◆Distance-time graphs can also represent accelerated motion, where the speed of the object changes over time.

◆In accelerated motion, the shape of the graph is nonlinear, indicating a non-uniform variation of distance with time.

7.4.2 VELOCITY-TIME GRAPH

Representation of Motion:

◆A velocity-time graph represents the variation in velocity of an object over time.

◆Time is plotted along the x-axis, while velocity is plotted along the y-axis.

Uniform Velocity:

◆If the object moves at uniform velocity, the height of its velocity-time graph remains constant with time.

◆The graph appears as a straight line parallel to the x-axis.

Calculating Displacement:

◆The area under the velocity-time graph and the time axis represents the displacement of the object.

◆For an object moving with uniform velocity, the displacement is equal to the area of the rectangle formed under the graph.

The formula to calculate displacement

s is given as

s = velocity ×time, which equals the area under the graph.

Uniformly Accelerated Motion:

◆For uniformly accelerated motion, the velocity-time graph is a straight line.

◆The velocity changes by equal amounts in equal intervals of time.

◆The area under the velocity-time graph represents the distance travelled by the object.

◆The formula to calculate displacement s in this case involves the area of both rectangle and triangle formed under the graph.

Non-Uniformly Accelerated Motion:

◆In non-uniformly accelerated motion, the velocity-time graph can have any shape.

7.5 Equations of Motion

7.6 Uniform Circular Motion

Uniform circular motion occurs when an object moves along a circular path at a constant speed. Here’s a breakdown of the key points regarding uniform circular motion:

Definition of Uniform Circular Motion:

Uniform circular motion is the motion of an object along a circular path at a constant speed, where the object’s velocity changes due to the change in direction of motion but not in magnitude.

Examples of Uniform Circular Motion:

◆The motion of an athlete running along a circular track at a constant speed.

◆The motion of a satellite in a circular orbit around a planet.

◆The motion of the moon and the earth in their respective orbits.

◆The motion of a cyclist on a circular track at a constant speed.

 Acceleration in Uniform Circular Motion:

◆Despite the constant speed, an object moving in uniform circular motion experiences acceleration.

◆This acceleration, known as centripetal acceleration, is directed towards the center of the circular path and is perpendicular to the velocity of the object.

Centripetal Force:

◆The force responsible for providing the necessary centripetal acceleration to keep an object moving in a circular path is called centripetal force.

◆Centripetal force is required to overcome the tendency of the object to move in a straight line due to its inertia.

Representation of Circular Motion:

Circular motion can be represented using equations that describe the relationship between the speed of the object, the radius of the circular path, and the time taken to complete one revolution.

The speed of an object in uniform circular motion is given by the formula:

v= 2πr/t  where v is the speed, r is the radius of the circular path, and t is the time taken to complete one revolution.

Release of Objects in Circular Motion:

When an object in uniform circular motion is released, it continues to move along the direction it was moving at the instant of release, tangential to the circular path.

This behaviour is observed in activities such as throwing a hammer or a discus in a sports meet, where the released object maintains its velocity and direction of motion.