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Scalar and Vector Quantities

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Definition:

• Scalar Quantity: A scalar quantity is a physical quantity that is completely described by its magnitude (size) only, without any reference to direction.
• Vector Quantity: A vector quantity is a physical quantity that has both magnitude (size) and direction.

Scalar Quantities:

• Mass: The mass of an object only requires a magnitude to describe it, e.g., 2 kg.
• Temperature: The temperature of a substance is a scalar quantity, e.g., 25°C.
• Time: The duration of an event is a scalar quantity, e.g., 10 seconds.

Vector Quantities:

• Displacement: The change in position of an object with direction, e.g., 5 meters east.
• Velocity: The rate of change of displacement with direction, e.g., 10 meters per second north.
• Force: A push or pull acting on an object with both magnitude and direction, e.g., 20 Newtons west.

Relative Velocity

• Relative velocity is the velocity of an object or observer in relation to another object, observer, or frame of reference.
• It represents the rate at which an object is moving with respect to another object.
• The relative velocity between two objects depends on their individual velocities and the angle between their paths.

Resolution of Vectors

Resolution into Two Perpendicular Directions:

• A vector can be resolved into two perpendicular components, typically horizontal and vertical components.
• The horizontal component is determined by multiplying the vector's magnitude by the cosine of the angle it makes with the horizontal axis.
• The vertical component is determined by multiplying the vector's magnitude by the sine of the angle it makes with the horizontal axis.

Graphical Methods of Solution:

• Graphical methods involve using a scale and drawing a vector diagram to determine the components of a vector.
• Draw the vector to scale, choose appropriate angles, and measure the lengths of the components using a ruler or compass.
• The sum of the components should give the original vector.

Objectives of the Notes:
Candidates should be able to:

• Distinguish between scalar and vector quantities.
• Give examples of scalar and vector quantities.
• Determine the resultant of two or more vectors.
• Determine relative velocity.
• Resolve vectors into two perpendicular components.
• Use graphical methods to solve vector problems.

Remember to practice solving problems related to these concepts to reinforce understanding and enhance problem-solving skills.