Class 11 Physics Notes

1. Vector Addition and Subtraction

Vector: Quantity with both magnitude and direction (e.g., velocity, displacement).

Scalar: Quantity with only magnitude (e.g., mass, time).

Addition of Vectors

• Triangle Law: Place the second vector's tail at the tip of the first vector.
• Parallelogram Law: Complete a parallelogram using the two vectors. Resultant = diagonal.

R = √(a² + b² + 2ab cos θ)

tan(α) = (b sin θ) / (a + b cos θ)

Subtraction of Vectors

a - b = a + (-b); where -b is the vector in the opposite direction of b.

Properties

• Commutative: a + b = b + a
• Associative: (a + b) + c = a + (b + c)

2. Projectile Motion

Motion of a body thrown into the air, moving under gravity in curved path (parabola).

Key Concepts

• Two-dimensional motion: Horizontal velocity is constant; vertical velocity is affected by gravity.

Formulas (Initial Velocity = u, Angle = θ)

u_x = u cos θ

u_y = u sin θ - gt

x = u cos θ × t

y = u sin θ × t - ½gt²

Time of Flight (T) = (2u sin θ) / g

Maximum Height (H) = u² sin² θ / (2g)

Range (R) = u² sin(2θ) / g

Path of projectile: Parabolic

3. Uniform Circular Motion

Motion in a circular path at constant speed. Direction of velocity changes constantly, so it's accelerated motion.

Important Concepts

• Centripetal Acceleration: Direction always toward center.
• Speed is constant, but velocity is changing.

Formulas

Centripetal Acceleration (a_c) = v² / r

Centripetal Force (F_c) = mv² / r

Time Period (T) = 2πr / v

Frequency (f) = 1 / T