UPCAT Physics — Newton's Laws, Dynamics & MomentumStudy Notes
Thorough study notes for Newton's Laws, Dynamics & Momentum — the fastest path from zero to ready for UPCAT Physics. Structured for self-study reviewers who cannot attend a review centre, these notes cover the full concept library plus the UPCAT-specific twists University of the Philippines adds to its questions.
Exam context
On the UPCAT 2026, the Physics subtest carries a "Core" weight in University of the Philippines's pattern. Newton's Laws, Dynamics & Momentum lands at position 3rd out of 6 in the standard review order. Target score is UPG ≤ 2.2 typical, and roughly 20 items come from Physics on a typical UPCAT paper.
Newton's Laws, Dynamics & Momentum - Study notes
Newton's Laws of Motion form the foundation of classical mechanics and help us understand how objects move in our everyday world. From a jeepney accelerating through EDSA to a basketball player jumping for a slam dunk, these laws explain the relationship between forces and motion. This chapter explores the three fundamental laws of motion, the concepts of dynamics and momentum, and their practical applications in the Philippine context.
Summary
Newton's Laws of Motion provide the fundamental framework for understanding dynamics and motion. The First Law (inertia) explains why objects resist changes in motion. The Second Law (F = ma) quantifies how forces produce acceleration. The Third Law describes action-reaction pairs that occur in all interactions. Momentum, defined as mass times velocity, is conserved in isolated systems and is particularly useful for analyzing collisions. Work, energy, and power concepts help us understand how forces transfer energy and accomplish tasks. These principles apply to everything from walking and transportation to sports and engineering applications throughout the Philippines and beyond.
Sections
Newton's First Law states that an object at rest stays at rest, and an object in motion stays in motion at constant velocity, unless acted upon by an unbalanced (net) force. This is also known as the Law of Inertia. Inertia is the tendency of objects to resist changes in their state of motion. Mathematically: If ΣF = 0 (net force is zero), then there is no change in motion. Inertia depends on mass - the more massive an object, the greater its inertia. This is why it's harder to push a loaded truck than an empty one.
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Newton's First Law of Motion (Law of Inertia)
Examples
- A passenger in a jeepney lurches forward when the driver suddenly brakes - the passenger's body continues moving due to inertia
- A coin placed on a card stays in place when you quickly flick the card away
- A basketball rolling on a smooth court continues rolling until friction stops it
Key Points
- Objects resist changes in motion (inertia)
- No net force means no change in velocity
- Mass determines the amount of inertia
- Both stationary and moving objects can be in equilibrium
Newton's Second Law quantifies the relationship between force, mass, and acceleration. It states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. Mathematical Formula: F = ma Where: F = net force (in Newtons, N), m = mass (in kg), a = acceleration (in m/s²) This law tells us that: - More force produces greater acceleration - Heavier objects need more force to achieve the same acceleration - The direction of acceleration is the same as the direction of the net force
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Newton's Second Law of Motion
Examples
- A tricycle needs more force to accelerate when carrying more passengers (greater mass)
- Kicking a soccer ball harder (more force) makes it accelerate faster
- A 50 N force applied to a 10 kg object produces 5 m/s² acceleration
Key Points
- F = ma is the fundamental equation of dynamics
- Force and acceleration are directly proportional
- Mass and acceleration are inversely proportional
- Net force determines acceleration, not just any single force
Newton's Third Law states that for every action, there is an equal and opposite reaction. When object A exerts a force on object B, object B simultaneously exerts an equal force in the opposite direction on object A. Key characteristics of action-reaction pairs: - Forces are equal in magnitude but opposite in direction - Forces act on different objects - Forces occur simultaneously - Both forces are the same type (contact, gravitational, etc.)
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Newton's Third Law of Motion (Action-Reaction)
Examples
- When you walk, you push backward on the ground, and the ground pushes forward on you
- A swimmer pushes water backward and the water pushes the swimmer forward
- When firing a gun, the bullet goes forward while the gun recoils backward
- Your weight pushes down on a chair, and the chair pushes up on you with normal force
Key Points
- Action and reaction forces are equal and opposite
- Forces act on different objects
- Both forces occur at the same time
- Explains how we walk, swim, and how rockets work
Understanding forces is crucial for analyzing motion. Common forces include: 1. Gravitational Force (Weight): W = mg, where g = 9.8 m/s² on Earth 2. Normal Force: The support force perpendicular to a surface 3. Friction Force: Opposes motion, depends on surface materials - Static friction: fs ≤ μsN (prevents motion) - Kinetic friction: fk = μkN (opposes motion) 4. Applied Force: Any external push or pull 5. Tension Force: Force transmitted through strings, ropes, or cables Free body diagrams help visualize all forces acting on an object, making it easier to apply Newton's laws.
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Forces and Free Body Diagrams
Examples
- A book on a table: Weight down, normal force up, forces balanced
- A jeepney on an inclined street: Weight, normal force, and friction all play roles
- A hanging basketball: Only weight and tension forces act on it
Key Points
- Weight always points toward Earth's center
- Normal force is perpendicular to contact surfaces
- Friction opposes motion or potential motion
- Free body diagrams show all forces on one object
- Net force determines acceleration using F = ma
Momentum (p) is a vector quantity that describes the 'quantity of motion' an object possesses. It equals mass times velocity: p = mv Momentum is particularly useful for analyzing collisions. The Law of Conservation of Momentum states that the total momentum of a system remains constant when no external forces act on it. For collisions: - Total momentum before = Total momentum after - m₁v₁ + m₂v₂ = m₁v₁' + m₂v₂' Types of collisions: 1. Elastic: Objects bounce apart, kinetic energy conserved 2. Inelastic: Objects stick together, some kinetic energy lost 3. Perfectly inelastic: Maximum energy loss, objects move together after collision
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Momentum and Its Conservation
Examples
- Two billiard balls colliding and bouncing apart (elastic collision)
- A moving car hitting a stationary car, both moving together afterward (inelastic)
- A basketball player catching a fast-moving ball gradually reduces its momentum
- Calculating the final velocities when two jeepneys collide
Key Points
- Momentum = mass × velocity (vector quantity)
- Momentum is conserved in isolated systems
- Larger mass or higher speed means greater momentum
- Impulse (force × time) changes momentum
- Conservation laws help solve collision problems
Work is done when a force causes displacement in the direction of the force: W = F × d × cos θ Where θ is the angle between force and displacement. Energy is the ability to do work. Key types: 1. Kinetic Energy: KE = ½mv² (energy of motion) 2. Potential Energy: PE = mgh (gravitational potential energy) 3. Mechanical Energy: Total KE + PE Power measures the rate of doing work: P = W/t = F·v Where P is power (watts), W is work (joules), and t is time (seconds). The Work-Energy Theorem states that work done equals change in kinetic energy.
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Work, Energy, and Power
Examples
- Lifting a sack of rice increases its gravitational potential energy
- A moving jeepney has kinetic energy proportional to its speed squared
- A falling coconut converts potential energy to kinetic energy
- A motor with higher power (horsepower) can do work faster
Key Points
- Work requires force and displacement in the same direction
- Energy is conserved but can change forms
- Kinetic energy depends on velocity squared
- Potential energy depends on height and mass
- Power measures how quickly work is done
Solving dynamics problems requires systematic approach: 1. Identify the system and draw free body diagrams 2. Choose coordinate axes appropriately 3. Apply Newton's laws: ΣF = ma for each direction 4. Use kinematics equations when needed 5. Check units and reasonableness of answers For momentum problems: 1. Identify the system and check if it's isolated 2. Calculate initial and final momenta 3. Apply conservation of momentum 4. Solve for unknown quantities Common problem types include: - Objects on inclined planes - Connected masses with pulleys - Collision analysis - Circular motion applications
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Applications and Problem-Solving
Examples
- Calculating the force needed to push a cart up a ramp
- Finding tension in a rope supporting a hanging load
- Determining stopping distance for a vehicle
- Analyzing the motion of a pendulum or yo-yo
Key Points
- Always start with clear diagrams
- Break forces into components when necessary
- Apply Newton's laws separately for each direction
- Conservation laws simplify complex problems
- Check that answers make physical sense
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