Laws of Motion - Formula Sheet

Key Formulas in Laws of Motion

Linear Momentum

p = m * v

• p = Linear momentum of the body (measured in kg m s-1)
• m = Mass of the body (measured in kg)
• v = Velocity of the body (measured in m s-1)

Newton's Second Law of Motion

F = m * a

• F = Net external force acting on the body (measured in Newtons, N)
• m = Mass of the body (measured in kg)
• a = Acceleration produced in the body (measured in m s-2)

Moment of a Force (Torque)

tau = F * d

• tau = Torque or moment of the force (measured in N m)
• F = Applied force (measured in N)
• d = Perpendicular distance from the fixed point or axis of rotation to the line of action of the force (measured in m)

Principle of Moments

F1 * d1 = F2 * d2

• F1, F2 = Parallel forces acting on the rigid body (measured in N)
• d1, d2 = Perpendicular distances of these forces from the fulcrum (measured in m)

Newton's Law of Universal Gravitation

F = G * (m1 * m2) / r^2

• F = Gravitational force of attraction between the two masses (measured in N)
• G = Universal gravitational constant (6.674 x 10-11 N m2 kg-2)
• m1, m2 = Masses of the two interacting bodies (measured in kg)
• r = Distance between the centers of the two masses (measured in m)

Acceleration due to Gravity at Earth's Surface

g = G * M / R^2

• g = Acceleration due to gravity (mean value of 9.8 m s-2 on Earth's surface)
• G = Universal gravitational constant (6.674 x 10-11 N m2 kg-2)
• M = Mass of the Earth (measured in kg)
• R = Radius of the Earth (measured in m)

Conservation of Linear Momentum (Collision of Two Bodies)

m1 * u1 + m2 * u2 = m1 * v1 + m2 * v2

• m1, m2 = Masses of the two colliding bodies (measured in kg)
• u1, u2 = Initial velocities of the bodies before collision (measured in m s-1)
• v1, v2 = Final velocities of the bodies after collision (measured in m s-1)

Apparent Weight in a Moving Lift

R = m * (g + a) (Moving upward with acceleration a)

R = m * (g - a) (Moving downward with acceleration a)

R = m * g (At rest or moving with uniform velocity)

R = 0 (Free fall under gravity alone, where a = g)

• R = Apparent weight or normal reaction force (measured in N)
• m = Mass of the person in the lift (measured in kg)
• g = Acceleration due to gravity (measured in m s-2)
• a = Acceleration of the lift (measured in m s-2)