Mass is the property of an object that resists changes in its motion.
Objects with larger mass require more force to produce a given acceleration.
3.1.2 Newton's second law of motion (F = ma):
The force acting on an object is equal to its mass multiplied by its acceleration.
The direction of acceleration and resultant force is always the same.
3.1.3 Linear momentum:
Linear momentum (p) is the product of an object's mass and velocity.
Linear momentum = mass × velocity (p = mv).
3.1.4 Force as the rate of change of momentum:
Force can be defined as the rate of change of momentum.
F = Δp/Δt (Force = change in momentum / change in time).
3.1.5 Newton's laws of motion:
Newton's first law (law of inertia): An object at rest or in motion will continue to remain in that state unless acted upon by an external force.
Newton's second law: The acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass.
Newton's third law: For every action, there is an equal and opposite reaction.
3.1.6 Weight:
Weight is the force experienced by an object due to a gravitational field.
Weight = mass × acceleration due to gravity (W = mg).
3.2 Non-uniform motion:
3.2.1 Frictional forces and drag forces:
Frictional forces oppose the motion of objects in contact with each other.
Drag forces (including air resistance) act on objects moving through a fluid and increase with speed.
3.2.2 Motion in a uniform gravitational field with air resistance:
Objects in a uniform gravitational field experience a downward force (weight) and may also experience an upward force due to air resistance.
The interplay of these forces affects the motion of objects.
3.2.3 Terminal velocity:
Objects moving against a resistive force (e.g., air resistance) may reach a terminal velocity.
Terminal velocity is a constant velocity achieved when the resistive force equals the driving force, resulting in zero net acceleration.
3.3 Linear momentum and its conservation:
3.3.1 Conservation of momentum:
The principle of conservation of momentum states that the total momentum of a system remains constant if no external forces act on it.
3.3.2 Applications of conservation of momentum:
Conservation of momentum can be applied to solve problems involving interactions between objects.
Elastic and inelastic collisions in one or two dimensions can be analyzed using the principle of conservation of momentum.
3.3.3 Perfectly elastic collisions:
In a perfectly elastic collision, the relative speed of approach between objects is equal to the relative speed of separation.
3.3.4 Change in kinetic energy:
While momentum of a system is always conserved in interactions between objects, some change in kinetic energy may take place due to external forces or internal energy transformations.