Ch 03 - Motion In A Plane11th Physics
Scalars vs. Vectors
What is the fundamental distinction between scalar and vector physical quantities in terms of properties and mathematical operations?
What is the fundamental distinction between scalar and vector physical quantities in terms of properties and mathematical operations?
- Scalars: Possess only magnitude (and unit). They strictly follow the rules of ordinary algebra (e.g., Mass, Temperature, Time, Distance).
- Vectors: Possess both magnitude and direction, and most importantly, they must explicitly obey the triangle law of addition (or equivalently, the parallelogram law) (e.g., Displacement, Velocity, Acceleration).
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Invariance of Scalars
Do scalar quantities change their value when the orientation of the coordinate axes is rotated? Can they be negative?
Do scalar quantities change their value when the orientation of the coordinate axes is rotated? Can they be negative?
Scalars are strictly invariant under the rotation of coordinate axes. Their value remains exactly the same for observers with different orientations of axes.
- Negative Values: Yes, scalar quantities can be negative.
- Example: Temperature can be , and Electric Charge can be . Magnitude-only does not restrict a scalar to purely positive values.
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The Null Vector
What is a 'Null Vector', and what are its magnitude and directional properties?
What is a 'Null Vector', and what are its magnitude and directional properties?
A Null (or Zero) Vector is a vector that has strictly zero magnitude and an arbitrary (undefined) direction.
- It is denoted by .
- Origins: It results from adding two equal and opposite vectors (), or by multiplying any valid vector by the real scalar number zero ().
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Also in this chapter
41 more cards to study in Prism
- 4Equality of Vectors
- 5Multiplying Vectors by Real Numbers
- 6Resultant Vector Magnitude (Law of Cosines)
- 7Unit Vectors
- 8Resultant Vector Direction
- 9Graphical Laws of Vector Addition
- 10Resolution of a Vector
- 11Analytical Vector Addition
- 12Position and Displacement in 2D
- 13Instantaneous Velocity in 2D
- 14Instantaneous Acceleration in 2D
- 15Position & Displacement Vectors
- 162D Kinematics: Velocity Equation
- 172D Kinematics: Position Equation
- 18Direction of Instantaneous Velocity
- 19Equation of Trajectory
- 20Time of Max Height & Time of Flight
- 21Independence of 2D Motion
- 22Maximum Height of a Projectile
- 23Horizontal Range of a Projectile
- 24Projectile Motion Characteristics
- 25Centripetal Acceleration
- 26Relative Velocity in 2D
- 27Maximum Range & Complementary Angles
- 28Angular Speed & Time Period
- 29Linear vs. Angular Speed
- 30Kinetic and Potential Energy at Maximum Height
- 31Projectile Launched from a Moving Platform
- 32Effect of Air Resistance on Projectile Trajectory
- 33Direction Cosines (3D Resolution)
- 34Relative Velocity: Rain-Umbrella Problem
- 35Projectile Velocity at Time 't'
- 36River-Boat Problem: Shortest Path
- 37River-Boat Problem: Shortest Time
- 38Vector Triangle Inequalities
- 39Nature of Uniform Circular Motion
- 40Condition for Perpendicular Vectors
- 41Time of Flight: Projectile on an Incline
- 42Average Acceleration in UCM over One Cycle
- 43Inapplicability of Standard Kinematic Equations to UCM
- 44Change in Velocity in UCM
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