• Vectors have both magnitude (size) and direction while scalars have magnitude but no direction.
• A vector is represented geometrically by an arrow drawn to scale.
• Addition of vectors also known as composition of vectors involves both the magnitude and direction of the vector.
• Resolution of vector means breaking the vector into its component vectors.
• A unit vector is a dimensionless vector having a magnitude of exactly one or unity.
• In projectile motion with no air resistance, a_x = 0 and a_y = -g.
• It is useful to think of projectile motion as the superposition of two motions:

1. constant-velocity motion in the x direction and
2. free-fall motion in the vertical direction subject to a constant downward acceleration of magnitude g = 9.8 m/s².

x = (v_o cosθ)t,
y = (v_o sinθ)t – ½ gt²
v_x = v_o cosθ
v_y = v_o sinθ – gt

• A particle in uniform circular motion travels around a circle or a circular arc at constant (uniform) speed.
• The acceleration associated with uniform circular motion that arises due to the change in direction of velocity is called centripetal a_c, where

• In non-uniform circular motion there is a component of acceleration that is parallel to the instantaneous velocity known as tangential acceleration a_t.
• The total acceleration, a is the resultant of the centripetal acceleration (a_c) and tangential acceleration (a_t).

• The net force causing the centripetal acceleration is the centripetal force

• Rotational motion is defined as the motion of a body about a fixed axis where all the particles constituting the body undergoes circular motion about a common axis.
• A rigid body is a body that can rotate with all its parts locked together and without any change in its shape.
• When a rigid object rotates about a fixed axis, every part of the object has the same angular speed and the same angular acceleration. The tangential values of velocity and acceleration depend on the distance of a point from the axis of rotation.
• Simple harmonic motion: type of oscillation in which acceleration is directly proportional to the displacement and directed toward the equilibrium position.

• The position, velocity and acceleration of a SHM as a function of time are
• For x = A, at t = 0, x = Acos(ωt + φ), v = −ωAsin(ωt + φ), a = − ω²Acos(ωt + φ),
• For x = 0, at t = 0, x = Asin(ωt + φ), v = ωAcos(ωt + φ), a = − ω²Asin(ωt + φ)
• Velocity of SHM as a function of displacement is

• Period of SHM is

and the frequency

• Period of simple pendulum of length is

and the frequency

• Resonance occurs when the frequency of the driving force equals the natural frequency of the oscillator.