Long Answer Questions — Chapter 1: Laws of Motion
Newton's First Law of Motion (Law of Inertia)
Statement: Every object continues to be in its state of rest or uniform motion in a straight line unless acted upon by a net external force.
- A body at rest will remain at rest unless a force is applied.
- A body moving with constant velocity in a straight line will continue to do so unless a force changes its state.
- This is also called the Law of Inertia.
Examples: 1. A book on a table stays at rest until someone pushes it. 2. A ball rolling on a frictionless surface would roll forever — friction is the external force that eventually stops it. 3. Passengers lurch backward when a bus starts suddenly.
Newton's Second Law of Motion (Law of Force and Acceleration)
Statement: The rate of change of momentum of a body is directly proportional to the net force applied and the change occurs in the direction of the force.
Mathematical Expression:
Let a body of mass m have initial velocity u and final velocity v after time t.
Initial momentum = mu Final momentum = mv Change in momentum = mv − mu Rate of change = (mv − mu) / t = m(v − u) / t = ma
Examples: 1. A cricket ball (small mass) accelerates more than a football (larger mass) for the same kick force. 2. A heavier truck requires a stronger engine (more force) to achieve the same acceleration as a car.
Newton's Third Law of Motion (Law of Action and Reaction)
Statement: For every action, there is an equal and opposite reaction. The action and reaction forces always act on two different bodies.
Key points:
- Action and reaction are simultaneous (occur at the same time)
- They are equal in magnitude and opposite in direction
- They act on different bodies — so they do not cancel each other
Examples: 1. Rocket propulsion: Hot gases are expelled backward (action) → rocket moves forward (reaction) 2. Walking: Foot pushes ground backward (action) → ground pushes foot forward (reaction) 3. Swimming: Swimmer pushes water backward (action) → water pushes swimmer forward (reaction) 4. Recoil of gun: Gun exerts force on bullet forward (action) → bullet exerts force on gun backward (reaction)
Statement: When no net external force acts on a system, the total momentum of the system remains constant.
Derivation:
Consider two balls A and B:
- Mass of A = mₐ, Mass of B = m_b
- Initial velocity of A = uₐ, Initial velocity of B = u_b
- They collide and after collision:
- Final velocity of A = vₐ, Final velocity of B = v_b
During collision:
Let F_AB = force exerted by A on B (action) Let F_BA = force exerted by B on A (reaction)
By Newton's Third Law: F_AB = −F_BA ... (1)
By Newton's Second Law:
- Change in momentum of B = F_AB × t = m_b(v_b − u_b)
- Change in momentum of A = F_BA × t = mₐ(vₐ − uₐ)
From equation (1): m_b(v_b − u_b) = −mₐ(vₐ − uₐ)
Expanding: m_b·v_b − m_b·u_b = −mₐ·vₐ + mₐ·uₐ
Rearranging: mₐ·uₐ + m_b·u_b = mₐ·vₐ + m_b·v_b
This means: Total initial momentum = Total final momentum
Therefore, momentum is conserved. ✓
Applications: 1. Recoil of a gun 2. Rocket and jet propulsion 3. Collisions between billiard balls
Situation: Before firing, both gun and bullet are at rest. The total momentum of the system = 0.
During firing:
- Explosion exerts force on the bullet → bullet moves forward with velocity v (say)
- By Newton's 3rd law, bullet exerts equal and opposite force on gun → gun moves backward
Applying conservation of momentum:
Total initial momentum = 0 (both at rest) Total final momentum = M × V + m × v
Where:
- M = mass of gun
- V = velocity of gun (recoil velocity, backward)
- m = mass of bullet
- v = velocity of bullet (forward)
Since total momentum is conserved: M × V + m × v = 0
V = −(m × v) / M
The negative sign indicates the gun moves in the opposite direction to the bullet.
Conclusion: The larger the mass of the gun (M), the smaller the recoil velocity (V). This is why heavy guns have less recoil compared to light guns.
Torque (Moment of Force)
Definition: Torque is the turning effect produced by a force on a body about an axis or pivot.
Where:
- τ = Torque (N·m)
- F = Force applied (N)
- d = Perpendicular distance from the pivot to the line of action of force (m)
Unit: Newton-metre (N·m)
Principle of Moments
Statement: When a body is in rotational equilibrium, the sum of clockwise moments about any point equals the sum of anticlockwise moments about the same point.
Mathematically: Sum of clockwise moments = Sum of anticlockwise moments
F₁ × d₁ = F₂ × d₂
Diagram Description (Lever / Seesaw):
- F₁ acts at distance d₁ on the left → creates anticlockwise moment = F₁ × d₁
- F₂ acts at distance d₂ on the right → creates clockwise moment = F₂ × d₂
- For equilibrium: F₁ × d₁ = F₂ × d₂
Types of Levers
| Type | Fulcrum position | Example |
|---|---|---|
| Class 1 | Between effort and load | Seesaw, scissors |
| Class 2 | Load between fulcrum and effort | Wheelbarrow, nutcracker |
| Class 3 | Effort between fulcrum and load | Tweezers, forearm |
Centripetal Force
Definition: The force that acts on a body moving in a circular path, always directed toward the centre of the circle, is called centripetal force.
Where:
- m = mass (kg)
- v = speed (m/s)
- r = radius (m)
Direction: Always toward the centre (inward)
Nature: Centripetal force is a real force — it is provided by some actual force in each case:
- Earth-Sun system: gravity provides centripetal force
- Stone on string: tension in string
- Car on road: friction with road surface
- Satellite in orbit: gravity provides centripetal force
Centrifugal Force
Definition: Centrifugal force is an apparent (pseudo) force that appears to act on a body moving in a circular path, directed away from the centre.
Nature: It is NOT a real force. It is a fictitious force that appears only in a rotating (non-inertial) reference frame.
Comparison Table
| Property | Centripetal Force | Centrifugal Force |
|---|---|---|
| Direction | Toward centre | Away from centre |
| Nature | Real force | Pseudo (fictitious) force |
| Cause | Provided by actual forces (gravity, tension, etc.) | Apparent, due to rotation |
| Exists in | All reference frames | Only in rotating frame |
| Example | Tension keeps stone in circular path | Mud flies off a spinning wheel |
Practical Applications of Centripetal/Centrifugal Effects
1. Road banking (curved roads): Roads are banked at an angle so the normal force provides centripetal force, allowing vehicles to turn safely. 2. Washing machine spin dry: Centrifugal effect throws water outward through holes in the drum. 3. Cream separator: Denser particles (milk) move outward, lighter cream stays inward when rotated. 4. Satellites: Gravity = centripetal force keeps satellites in orbit.
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