LAWS OF MOTION

1. Newton's First Law of Motion: Also known as the law of inertia, it states that an object at rest will remain at rest, and an object in motion will continue to move with a constant velocity unless acted upon by an external force.
2. Newton's Second Law of Motion: It states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. The formula for Newton's second law is: F = ma, where F is the net force, m is the mass of the object, and a is the acceleration produced.
3. Newton's Third Law of Motion: It states that every action has an equal and opposite reaction. When an object exerts a force on another object, the second object exerts an equal and opposite force on the first object.
4. Inertia: It is the property of an object to resist changes in its motion. The greater the mass of an object, the greater its inertia.
5. Friction: It is the force that opposes the relative motion between two objects in contact. It can act in the direction opposite to the motion or impending motion of an object.
6. Types of Forces: Forces can be classified as contact forces (such as friction, normal force, tension, etc.) and non-contact forces (such as gravitational force, electromagnetic force, etc.).
7. Free Body Diagrams: These diagrams are used to represent the forces acting on an object in a graphical manner, with arrows showing the direction and magnitude of each force.
8. Momentum: It is the product of an object's mass and velocity. The formula for momentum is: p = mv, where p is the momentum, m is the mass of the object, and v is its velocity.
9. Impulse: It is the change in momentum of an object when a force acts upon it for a certain period of time. The formula for impulse is: J = Δp = FΔt, where J is the impulse, Δp is the change in momentum, F is the force, and Δt is the time for which the force acts.
10. Conservation of Momentum: According to the law of conservation of momentum, the total momentum of an isolated system remains constant if no external forces act on it.
11. Circular Motion: Objects in circular motion experience centripetal force directed towards the center of the circle. It is provided by a net inward force acting on the object.
12. Equilibrium: When the net force on an object is zero, it is in a state of equilibrium. There are two types of equilibrium: static equilibrium (when the object is at rest) and dynamic equilibrium (when the object is moving with a constant velocity).
13. Applications of Laws of Motion: The principles of Newton's laws of motion are applied in various real-life scenarios, such as vehicle motion, sports, space exploration, etc.

14. Torque: It is the turning force applied to an object about an axis of rotation. The formula for torque is: τ = r × F, where τ is the torque, r is the distance from the axis of rotation to the point where the force is applied, and F is the force applied.
15. Angular Momentum: It is the rotational equivalent of linear momentum and is defined as the product of moment of inertia and angular velocity. The formula for angular momentum is: L = Iω, where L is the angular momentum, I is the moment of inertia, and ω is the angular velocity.
16. Moment of Inertia: It is a measure of an object's resistance to rotational motion and depends on its shape and mass distribution. Different objects have different formulas for moment of inertia, such as I = 1/3 mL^2 for a solid sphere, I = 1/2 mL^2 for a solid cylinder, etc.
17. Coefficient of Restitution: It is a measure of how elastic a collision between two objects is. It is defined as the ratio of the relative velocity of separation to the relative velocity of approach. The formula for coefficient of restitution is: e = (v2f - v1f)/(v1i - v2i), where e is the coefficient of restitution, v1i and v2i are the initial velocities of the colliding objects, and v1f and v2f are their final velocities after collision.
18. Free Fall: It is the motion of an object under the influence of only gravitational force. The acceleration due to gravity on Earth is denoted by "g" and is approximately equal to 9.8 m/s^2.
19. Terminal Velocity: It is the maximum velocity that an object reaches while falling through a fluid (such as air) due to the balance between the gravitational force and the air resistance. The formula for terminal velocity is: v = (mg/cd)^0.5, where v is the terminal velocity, m is the mass of the object, g is the acceleration due to gravity, cd is the drag coefficient, and A is the cross-sectional area of the object.
20. Projectile Motion: It is the motion of an object that is projected into the air and moves under the influence of both horizontal and vertical forces. The horizontal motion is uniform, while the vertical motion is under the influence of gravity, resulting in a parabolic path.

21. Newton's Third Law of Motion: It states that for every action, there is an equal and opposite reaction. This means that whenever one object exerts a force on another object, the second object exerts an equal and opposite force back on the first object. Mathematically, F1 on 2 = -F2 on 1, where F1 on 2 is the force exerted by object 1 on object 2, and F2 on 1 is the force exerted by object 2 on object 1.
22. Conservation of Linear Momentum: It states that the total linear momentum of a system of particles remains constant if no external forces act on the system. Mathematically, Σpi = Σpf, where Σpi is the initial total linear momentum of the system, and Σpf is the final total linear momentum of the system.
23. Impulse: It is the change in momentum of an object when a force acts on it for a certain period of time. The formula for impulse is: J = FΔt, where J is the impulse, F is the force, and Δt is the time for which the force acts.
24. Elastic Collision: It is a collision in which the total kinetic energy and momentum of the system are conserved. Mathematically, mv1i + mv2i = mv1f + mv2f, where m is the mass of the objects, v1i and v2i are the initial velocities, and v1f and v2f are the final velocities after collision.
25. Inelastic Collision: It is a collision in which the total kinetic energy of the system is not conserved, but momentum is conserved. Mathematically, mv1i + mv2i = mv1f + mv2f, where m is the mass of the objects, v1i and v2i are the initial velocities, and v1f and v2f are the final velocities after collision.
26. Newton's Law of Universal Gravitation: It states that every object in the universe attracts every other object with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers. The formula for gravitational force is: F = G * (m1 * m2) / r^2, where F is the gravitational force, G is the universal gravitational constant, m1 and m2 are the masses of the objects, and r is the distance between their centers.
27. Gravitational Potential Energy: It is the energy possessed by an object due to its position in a gravitational field. The formula for gravitational potential energy is: U = m * g * h, where U is the gravitational potential energy, m is the mass of the object, g is the acceleration due to gravity, and h is the height of the object above the reference point.
28. Escape Velocity: It is the minimum velocity that an object must have in order to escape the gravitational pull of a planet or a celestial body. The formula for escape velocity is: ve = (2 * G * M / R)^0.5, where ve is the escape velocity, G is the universal gravitational constant, M is the mass of the planet or celestial body, and R is the radius of the planet or celestial body.

29. Circular Motion: When an object moves in a circular path, it experiences a centripetal force that keeps it moving in a circle. The formula for centripetal force is: Fc = (mv^2) / r, where Fc is the centripetal force, m is the mass of the object, v is the velocity of the object, and r is the radius of the circular path.
30. Banked Curve: A banked curve is a curved road or track that is inclined towards the center of the circle to allow vehicles to safely navigate the curve without skidding. The formula for the angle of banking (θ) of a banked curve is: tanθ = (v^2) / (r * g), where θ is the angle of banking, v is the speed of the vehicle, r is the radius of the curve, and g is the acceleration due to gravity.
31. Friction: Friction is the force that opposes the motion of an object when it moves over a surface or through a medium. It depends on the nature of the surfaces in contact, the normal force, and the coefficient of friction. The formulas for friction are:

• Static friction (fs): fs ≤ μs * N, where μs is the coefficient of static friction, and N is the normal force.
• Kinetic friction (fk): fk = μk * N, where μk is the coefficient of kinetic friction, and N is the normal force.

• Terminal Velocity: Terminal velocity is the maximum velocity that an object reaches when falling through a fluid (like air or water) due to the opposing force of air resistance. The formula for terminal velocity is: vt = (2 * m * g) / (ρ * Cd * A)^0.5, where vt is the terminal velocity, m is the mass of the object, g is the acceleration due to gravity, ρ is the density of the fluid, Cd is the drag coefficient, and A is the cross-sectional area of the object.
• Conservation of Energy: It states that the total energy of a closed system remains constant. In a mechanical system, the sum of kinetic energy and potential energy remains constant. Mathematically, Ki + Ui = Kf + Uf, where Ki and Kf are the initial and final kinetic energies, and Ui and Uf are the initial and final potential energies.
• Work-Energy Principle: It states that the work done on an object is equal to the change in its kinetic and potential energies. The formula for work (W) is: W = ΔK + ΔU, where ΔK is the change in kinetic energy, and ΔU is the change in potential energy.
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  1. Newton's First Law of Motion: An object at rest tends to stay at rest, and an object in motion tends to stay in motion with the same velocity, unless acted upon by an external force.
  2. Newton's Second Law of Motion: The net force acting on an object is equal to the product of its mass and acceleration. The formula is: F = m * a, where F is the net force, m is the mass of the object, and a is the acceleration.
  3. Newton's Third Law of Motion: For every action, there is an equal and opposite reaction.
  4. Centripetal Force: The force that keeps an object moving in a circular path. The formula is: Fc = (mv^2) / r, where Fc is the centripetal force, m is the mass of the object, v is the velocity of the object, and r is the radius of the circular path.
  5. Gravity: The force of attraction between two objects due to their masses. The formula is: Fg = (G * (m1 * m2)) / r^2, where Fg is the gravitational force, G is the universal gravitational constant, m1 and m2 are the masses of the two objects, and r is the distance between their centers.
  6. Friction: The force that opposes the motion of an object. The formulas are:
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  • Static friction (fs): fs ≤ μs * N, where μs is the coefficient of static friction, and N is the normal force.
  • Kinetic friction (fk): fk = μk * N, where μk is the coefficient of kinetic friction, and N is the normal force.

7. Momentum: The product of an object's mass and velocity. The formula is: p = m * v, where p is the momentum, m is the mass of the object, and v is its velocity.
8. Impulse: The change in momentum of an object due to an applied force. The formula is: J = Δp = F * Δt, where J is the impulse, Δp is the change in momentum, F is the applied force, and Δt is the time for which the force is applied.
9. Work: The product of the force applied on an object and the displacement of the object in the direction of the force. The formula is: W = F * d * cosθ, where W is the work done, F is the applied force, d is the displacement, and θ is the angle between the force and displacement vectors.
10. Kinetic Energy: The energy possessed by an object due to its motion. The formula is: KE = (1/2) * m * v^2, where KE is the kinetic energy, m is the mass of the object, and v is its velocity.
11. Potential Energy: The energy possessed by an object due to its position in a force field. The formula is: PE = m * g * h, where PE is the potential energy, m is the mass of the object, g is the acceleration due to gravity, and h is the height or displacement from a reference point.

Conservation of Energy: The total energy of a closed system remains constant. In a mechanical system, the sum of kinetic energy and potential energy remains constant. Mathematically, Ki + Ui = Kf + Uf, where Ki and Kf are the initial and final kinetic energies, and Ui and Uf are the initial and final potential energies.

13. Torque: The turning effect of a force about a point or axis. The formula is: τ = r * F * sinθ, where τ is the torque, r is the perpendicular distance from the point or axis to the line of action of the force, F is the applied force, and θ is the angle between the force and the displacement vectors.
14. Angular Momentum: The rotational equivalent of linear momentum. The formula is: L = I * ω, where L is the angular momentum, I is the moment of inertia, and ω is the angular velocity.
15. Moment of Inertia: The resistance of an object to rotational motion. The formula depends on the shape and mass distribution of the object and is different for different objects.
16. Elasticity: The property of a material to return to its original shape and size after deformation. The formulas are:

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   • Hooke's Law: F = k * ΔL, where F is the restoring force, k is the spring constant, and ΔL is the change in length or deformation.
   • Young's Modulus: Y = (F/A) / (ΔL/L), where Y is the Young's modulus, F is the applied force, A is the cross-sectional area, ΔL is the change in length or deformation, and L is the original length of the object.
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   17. Newton's Law of Universal Gravitation: The law that describes the gravitational force between two point masses. The formula is: Fg = (G * (m1 * m2)) / r^2, where Fg is the gravitational force, G is the universal gravitational constant, m1 and m2 are the masses of the two objects, and r is the distance between their centers.