Motion class 9 Short Notes Chapter 7, Easy And Keyword Focused!

“Motion class 9 Short Notes Chapter 7, Easy And Keyword Focused!” is prepared from the NCERT text book. All the questions in your examinations are framed on the basis of this book.

MOTION: Fundamental Concepts

• Definition of Motion: We often perceive an object to be in motion when its position changes with time.
  • Motion can also be inferred through indirect evidences (e.g., motion of air by observing dust or leaves).
• Relativity of Motion: An object may appear to be moving for one person and stationary for another (e.g., roadside trees appear to move backwards for bus passengers, while a person on the road sees the bus moving).
• Types of Motion: Most motions are complex. Some common types include:
  • Straight line motion.
  • Circular path motion.
  • Rotation.
  • Vibration.
  • Situations can involve a combination of these.

Describing Motion

• Reference Point/Origin: To describe the location or position of an object, we must specify a reference point, also called the origin.
  • Example: A school is 2 km north of the railway station, making the railway station the reference point.
• Motion Along a Straight Line: This is the simplest type of motion.

Distance and Displacement

• Distance:
  • The total path length covered by the object.
  • To describe distance, we need to specify only its numerical value (magnitude).
  • Magnitude: The numerical value of a physical quantity.
  • Example: An object moving from O to A (60 km) and then to C (35 km from A) covers a total distance of 60 km + 35 km = 95 km.
  • An odometer in automobiles shows the distance travelled.
• Displacement:
  • The shortest distance measured from the initial to the final position of an object.
  • The magnitude of displacement can be equal to or less than the distance travelled.
  • Zero Displacement: The magnitude of displacement can be zero even if the corresponding distance covered is not zero.
    • Example: If an object travels from O to A (60 km) and then back to O, the final position coincides with the initial position, so the displacement is zero, but the distance covered is 120 km (60 km + 60 km).

Uniform and Non-Uniform Motion

• Uniform Motion: An object is in uniform motion if it covers equal distances in equal intervals of time. The time interval should be small.
  • Velocity: During uniform motion along a straight line, the velocity remains constant with time. The change in velocity is zero.
• Non-Uniform Motion: Objects are in non-uniform motion when they cover unequal distances in equal intervals of time.
  • Examples: A car on a crowded street or a person jogging in a park.
  • Velocity: In non-uniform motion, velocity varies with time and has different values at different instants and points.

Measuring the Rate of Motion: Speed and Velocity

• Speed:
  • The distance travelled by the object in unit time.
  • To specify speed, only its magnitude is required.
  • SI Unit: metre per second (m s⁻¹ or m/s).
  • Other units: centimetre per second (cm s⁻¹) and kilometre per hour (km h⁻¹).
• Average Speed: Used when objects are in non-uniform motion.
  • Formula: Average speed = Total distance travelled / Total time taken v = s / t
  • Example: Car travels 100 km in 2 h, average speed is 50 km h⁻¹.
• Velocity:
  • The speed of an object moving in a definite direction.
  • Specifies both speed and its direction of motion.
  • Can be uniform or variable.
  • Can be changed by changing the object’s speed, direction of motion, or both.
  • SI Unit: m s⁻¹ or m/s (same as speed).
• Average Velocity:
  • For an object moving along a straight line at a variable speed, it’s calculated similar to average speed.
  • If the velocity of the object is changing at a uniform rate, average velocity is the arithmetic mean of initial velocity and final velocity.
    • Formula: Average velocity = (initial velocity + final velocity) / 2
    •  v_av = (u + v) / 2
• Distinction between Speed and Velocity: Speed requires only magnitude, while velocity specifies both magnitude (speed) and direction. Average speed and average velocity can be different (e.g., Usha swimming 180 m in a 90 m pool and returning to start: average speed = 3 m/s, average velocity = 0 m/s).

Acceleration : Rate of Change of Velocity

• Acceleration:
  • A measure of the change in the velocity of an object per unit time.
  • Formula: acceleration = change in velocity / time taken a = (v – u) / t (where u = initial velocity, v = final velocity, t = time)
  • SI Unit: m s⁻².
  • Direction: Taken as positive if in the direction of velocity, and negative when opposite to the direction of velocity.
• Accelerated Motion: Motion where velocity changes.
• Uniform Acceleration: An object travels in a straight line, and its velocity increases or decreases by equal amounts in equal intervals of time.
  • Example: Motion of a freely falling body.
• Non-Uniform Acceleration: Velocity changes at a non-uniform rate.
  • Example: A car on a straight road increasing its speed by unequal amounts in equal time intervals.

Graphical Representation of Motion

• Purpose: Graphs provide a convenient method to present basic information and show the dependence of one physical quantity (like distance or velocity) on another (like time).
• Axes: Time is taken along the x-axis, and distance or velocity is taken along the y-axis.

Distance-Time Graphs

• Uniform Speed: The graph of distance travelled against time is a straight line. This shows distance is directly proportional to time. (Fig. 7.3)
• Determining Speed: The speed (v) of an object from a distance-time graph is calculated as the slope of the line: v = (s₂ – s₁) / (t₂ – t₁)
• Non-Uniform Speed (Accelerated Motion): The distance-time graph shows a non-linear variation of distance with time. The shape is different from uniform motion. (Fig. 7.4)
• Object at Rest: A distance-time graph that is a straight line parallel to the time axis indicates that the object is at rest (not moving).

Velocity-Time Graphs

• Uniform Velocity: The velocity-time graph is a straight line parallel to the x-axis (time axis). (Fig. 7.5)
• Displacement (Magnitude) from Velocity-Time Graph: The area enclosed by the velocity-time graph and the time axis is equal to the magnitude of the displacement (distance moved).
  • For uniform velocity: s = Area of rectangle (velocity × time interval).
• Uniformly Accelerated Motion: The velocity-time graph is a straight line. (Fig. 7.6)
  • The area under this graph (e.g., a trapezoid or rectangle + triangle) gives the distance (magnitude of displacement).
    • s = Area ABCDE = Area of rectangle ABCD + Area of triangle ADE = (AB × BC) + ½ (AD × DE)
• Non-Uniformly Accelerated Motion: Velocity-time graphs can have any shape. (Fig. 7.7)

Equations of Motion (for Uniform Acceleration)

• For an object moving along a straight line with uniform acceleration, three equations relate its velocity, acceleration, distance, and time.
• Variables:
  1. u: Initial velocity.
  2. v: Final velocity.
  3. a: Uniform acceleration.
  4. t: Time.
  5. s: Distance travelled.
• Equations:
  1. Velocity-time relation: v = u + at
  2. Position-time relation: s = ut + ½ at²
  3. Position-velocity relation: 2as = v² – u²

Uniform Circular Motion

• Acceleration in Circular Motion: When an object moves along a circular path with constant magnitude of velocity (uniform speed), its direction of motion changes continuously. This continuous change in direction means the object is accelerating.
• Uniform Circular Motion: Occurs when an object moves in a circular path with uniform speed.
• Speed Formula for Circular Path: If an object takes t seconds to go once around a circular path of radius r, its speed v is given by: v = 2πr / t
  • 2πr is the circumference of the circle.
• Examples: Athlete throwing a hammer/discus, motion of the moon and the Earth, a satellite in a circular orbit, a cyclist on a circular track at constant speed.

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