FORCE AND LAWS OF MOTION – Formula & Equation Sheet
Essential formulas and equations from Science, tailored for Class 9 in Science.
This one-pager compiles key formulas and equations from the FORCE AND LAWS OF MOTION chapter of Science. Ideal for exam prep, quick reference, and solving time-bound numerical problems accurately.
Key concepts & formulas
Essential formulas, key terms, and important concepts for quick reference and revision.
Formulas
F = ma
F is the force (in newtons), m is mass (in kg), and a is acceleration (in m/s²). This fundamental relation expresses how force affects motion, demonstrating that greater force results in higher acceleration.
p = mv
p is momentum (in kg·m/s), m is mass (in kg), and v is velocity (in m/s). This formula defines momentum, highlighting its dependency on both mass and speed of an object.
v = u + at
v is final velocity (m/s), u is initial velocity (m/s), a is acceleration (m/s²), and t is time (s). Useful to calculate an object's velocity after acceleration over time.
s = ut + 1/2at²
s is distance (m), u is initial velocity (m/s), a is acceleration (m/s²), t is time (s). This equation computes the distance traveled under uniform acceleration.
F_friction ≤ μN
F_friction is the frictional force (N), μ is the coefficient of friction, and N is the normal force (N). This inequality describes the maximum static friction before movement occurs.
a = (v - u) / t
a is acceleration (m/s²), v is final velocity (m/s), u is initial velocity (m/s), and t is time (s). This formula shows the relationship between change in velocity and time.
W = Fd cos(θ)
W is work done (in joules), F is the applied force (N), d is displacement (m), and θ is the angle between the force and displacement direction. This measures work done when force moves an object.
P = F / A
P is pressure (Pa), F is force (N), and A is area (m²). This formula relates force exerted on an area to pressure, useful for understanding pneumatic systems.
1 N = 1 kg·m/s²
This defines the newton, the unit of force. It expresses that one newton is the force required to accelerate a one-kilogram mass by one meter per second squared.
Newton's First Law: Objects in motion tend to stay in motion.
This law states that an object will remain at rest or in uniform motion unless acted upon by a net external force, emphasizing inertia.
Equations
ΣF = ma
ΣF is the net force (N), proportional to the mass and acceleration of an object. This foundational principle governs motion, stating that the sum of forces results in acceleration.
F_net = F_applied - F_friction
This equation calculates the net force acting on an object, factoring in applied force and opposing friction, essential for predicting motion.
v² = u² + 2as
This equation determines final velocity based on initial velocity, acceleration, and distance, significant in uniform acceleration scenarios.
m₁v₁ + m₂v₂ = (m₁ + m₂)v_f
This conservation of momentum equation relates the momenta of two colliding objects to their combined final velocity, crucial in collision problems.
F = -kx
F is restoring force (N), k is the spring constant (N/m), and x is extension or compression (m). This Hooke's law describes the behavior of springs.
E_k = 1/2 mv²
E_k is kinetic energy (joules), m is mass (kg), v is velocity (m/s). This formula calculates kinetic energy, relevant in dynamics.
E_p = mgh
E_p is potential energy (joules), m is mass (kg), g is acceleration due to gravity (9.8 m/s²), h is height (m). This calculates gravitational potential energy.
F = G(m₁m₂)/r²
F is the gravitational force (N), G is the gravitational constant, m₁ and m₂ are masses (kg), r is distance (m). This equation quantifies gravitational attraction.
Q = mcΔT
Q is heat energy (J), m is mass (kg), c is specific heat capacity (J/kg·°C), ΔT is temperature change (°C). This formula expresses the heat transfer in thermal processes.
F = ma (Newton's Second Law)
This reinforces the concept that net force results in acceleration, where force is calculated by multiplying mass and acceleration.
