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This chapter explores the foundational laws governing motion, focusing on how forces affect the movement of objects, which is crucial for understanding physics.
LAWS OF MOTION – Formula & Equation Sheet
Essential formulas and equations from Physics Part - I, tailored for Class 11 in Physics.
This one-pager compiles key formulas and equations from the LAWS OF MOTION chapter of Physics Part - I. 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 net external force (N), m is mass (kg), and a is acceleration (m/s²). This formula represents Newton's second law of motion showing the relationship between force, mass, and acceleration.
p = mv
p represents momentum (kg m/s), m is mass (kg), and v is velocity (m/s). It defines momentum as the product of mass and velocity, a key concept in understanding motion.
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). This kinematic equation relates velocity, acceleration, and time.
s = ut + 0.5at²
s is distance (m), u is initial velocity (m/s), a is acceleration (m/s²), and t is time (s). This formula calculates distance traveled under constant acceleration.
F_s ≤ μ_s N
F_s is static friction (N), μ_s is the coefficient of static friction, and N is the normal force (N). This relation describes the maximum static friction force before motion begins.
f_k = μ_k N
f_k is kinetic friction (N), μ_k is the coefficient of kinetic friction, and N is the normal force (N). This formula defines kinetic friction once an object is in motion.
ΣF = 0
The sum of all forces (ΣF) acting on a particle in equilibrium is zero. This condition is necessary for an object to be at rest or in uniform motion.
t = Δp / F
t is time (s), Δp is change in momentum (kg m/s), and F is the average force (N). This relationship illustrates the time over which force acts to bring about a change in momentum.
F_c = m(v²/R)
F_c is centripetal force (N), m is mass (kg), v is tangential speed (m/s), and R is radius of circular path (m). This formula calculates the centripetal force necessary for circular motion.
p_{before} = p_{after}
This principle states that in an isolated system, the total momentum before an interaction (collision) is equal to the total momentum after the interaction, embodying the conservation of momentum.
Equations
F_{net} = F_{applied} - F_{friction}
This equation describes the net force acting on an object as the difference between the applied force and the frictional force acting in the opposite direction.
W = mg
W is weight (N), m is mass (kg), and g is gravitational acceleration (approximately 9.8 m/s² on Earth). This formula determines the weight of an object due to gravity.
a = (v_f - v_i) / t
a is acceleration (m/s²), v_f is final velocity (m/s), v_i is initial velocity (m/s), and t is time (s). This formula calculates acceleration as the change in velocity over time.
F_{gravity} = G(m_1m_2)/r^2
This is the law of universal gravitation where F_{gravity} is the gravitational force (N), G is gravitational constant (6.674 × 10⁻¹¹ N m²/kg²), m_1 and m_2 are the masses (kg), and r is the distance between their centers (m).
T = f_s + f_k
T is the total tension in a string, f_s is static friction, and f_k is kinetic friction. This relationship shows the forces acting on an object in motion in a string setup.
v_o = √(Rg tan θ)
v_o is the optimal speed on a banked road, R is the radius (m), g is gravitational acceleration (9.8 m/s²), and θ is the banking angle (degrees). This equation helps find the ideal speed to maintain frictionless motion on a curve.
p_A + p_B before = p_A' + p_B' after
This law describes that total momentum before a collision (p_A + p_B) equals total momentum after the collision (p_A' + p_B'), applicable for elastic and inelastic collisions.
T = 2rπf
T is the period of revolution (s), r is radius (m), π is a constant (≈ 3.14), and f is frequency (Hz). This formula finds the period of a revolving object in circular motion.
θ = tan⁻¹(μ_s)
This formula calculates the maximum angle θ (degrees) at which an object will remain at rest on an inclined plane without slipping, where μ_s is the coefficient of static friction.
F_{net\_circular} = m(v^2/R)
This net force acting in circular motion states that the centripetal force is mass times the square of tangential speed divided by the radius.
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