• Galileo observed that objects on an inclined plane move with constant speed when no force acts on them.
• When a marble rolls down an inclined plane, its velocity increases due to the unbalanced force of gravity.
• The marble's velocity decreases as it climbs up the inclined plane.

• Galileo proposed an experiment with a marble on a frictionless inclined plane.
• If released from one side, the marble would roll down, climb up the opposite side, and reach the same height.
• Decreasing the inclination angle of one side would cause the marble to travel further distances.
• If one side is made horizontal, the marble would continue traveling indefinitely due to zero unbalanced forces.

• Newton formulated three fundamental laws of motion.
• The first law states that an object remains in a state of rest or uniform motion unless acted upon by an external force.
• This is known as the law of inertia, where objects resist changes in their state of motion.

• Experiences in motorcars can be explained by the law of inertia.
• For example, passengers tend to remain at rest until acted upon by braking or acceleration forces.
• Safety belts prevent injuries by exerting forces to slow down the body's motion.
• When a motorcar makes a sharp turn, passengers tend to move to one side due to their inertia.

• Activities can be conducted to illustrate the first law, demonstrating that objects remain at rest unless acted upon by unbalanced forces.

9.3 Inertia and Mass

Inertia:

• Inertia is the property of an object that resists changes in its state of motion.
• If an object is at rest, it tends to remain at rest; if it's in motion, it tends to keep moving.

Variation in Inertia:

• Not all bodies have the same inertia.
• For example, it's easier to push an empty box than a box full of books, and a football flies away when kicked, while a stone hardly moves.
• The amount of force needed to change the motion of an object depends on its inertia.

Relation to Mass:

• Heavier or more massive objects offer larger inertia.
• Inertia is quantitatively measured by mass.
• Mass is a measure of the amount of matter in an object, and it directly relates to its inertia.

Inertia and Mass:

• Inertia is the natural tendency of an object to resist changes in its state of motion or rest.
• The mass of an object serves as a measure of its inertia, with heavier objects having greater inertia.

9.4 Second Law of Motion

Introduction to First Law and Momentum:

• The first law of motion indicates that an unbalanced external force acting on an object changes its velocity, resulting in acceleration.
• Newton introduced the concept of momentum to quantify the combined effect of an object's mass and velocity.
• Momentum (p) is defined as the product of an object's mass (m) and velocity (v): p = mv.

Properties of Momentum:

• Momentum has both direction and magnitude, with its direction aligned with the object's velocity.
• The SI unit of momentum is kilogram-meter per second (kg m/s).
• Applying an unbalanced force changes an object's velocity, thus changing its momentum.

Effect of Force and Time on Momentum:

• The impact produced by objects depends on their mass and velocity.
• A force produces a change in momentum, and the magnitude of this change depends not only on the force's magnitude but also on the time over which it is exerted.
• The force necessary to change an object's momentum depends on the rate at which the momentum changes.

Second Law of Motion:

• The second law of motion states that the rate of change of momentum of an object is proportional to the applied unbalanced force in the direction of the force.

9.4.1 MATHEMATICAL FORMULATION OF SECOND LAW OF MOTION

9.5 Third Law of Motion

Third Law of Motion:

• The third law of motion states that for every action, there is an equal and opposite reaction.
• When one object exerts a force on another object, the second object instantaneously exerts a force back on the first.
• These action and reaction forces are equal in magnitude but opposite in direction, acting on different objects.
• In scenarios like a collision in football, both parties involved exert forces on each other, resulting in mutual impacts.

Demonstration with Spring Balances:

• Connecting two spring balances demonstrates the third law of motion.
• When a force is applied through one balance, both show equal readings, indicating action and reaction forces between them.
• The force exerted by one balance on the other is the action, and the force exerted by the other balance in response is the reaction.

Application in Everyday Situations:

• When walking, the force applied to accelerate isn't directed forward but is exerted against the ground, leading to an equal and opposite reaction, propelling the person forward.
• Action and reaction forces, though equal in magnitude, may not produce equal accelerations due to differences in mass.

Illustrations:

• Examples like firing a gun, where the recoil of the gun illustrates action and reaction forces with different accelerations due to mass differences.
• A sailor jumping from a boat demonstrates action and reaction forces, where the force on the boat moves it backward as the sailor moves forward.

Demonstration with Carts:

• Placing children on different carts and applying the same force illustrates different accelerations due to differences in mass, complying with the second law of motion.
• Constructing a Demonstrative Cart:
• A cart for the demonstration can be constructed using plywood and ball-bearing wheels.