Forces and Motion – Interactive Study Guide

⚡ Forces and Motion ⚡

Interactive Study Guide

📚 0/9 Topics
✅ 0/9 Quizzes

1 Speed and Velocity

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📖 What’s the Difference?

Speed is how fast something moves – just a number with units (like 60 km/h).
Velocity is speed in a specific direction – needs both magnitude and direction (like 60 km/h north).

🔢 Key Formulas

speed = distance ÷ time
v = s / t
Formula What it means
v = s / t Standard symbols version
average speed = total distance ÷ total time Used when speed changes during journey

💡 Worked Example

Problem: A car travels 120 km in 2 hours. What is its average speed?
• Distance = 120 km
• Time = 2 hours
• Speed = distance ÷ time = 120 ÷ 2 = 60 km/h

💡 Study Tips

Always write down the units (m/s, km/h, etc.)
If units don’t match, convert them first!
Remember: velocity needs direction (e.g., 60 km/h north)
🎯 Quick Quiz
A cyclist travels 30 km in 1.5 hours. What is their average speed?
A) 15 km/h
B) 20 km/h
C) 25 km/h
D) 45 km/h

2 Acceleration

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📖 Understanding Acceleration

Acceleration is the rate of change of velocity. It tells us how quickly something is speeding up or slowing down.

🔢 Key Formulas

a = (v – u) ÷ t
where: a = acceleration, v = final velocity, u = initial velocity, t = time
Formula What it means
v = u + at Final velocity from initial velocity
s = ut + ½at² Distance traveled with acceleration

💡 Worked Example

Problem: A car accelerates from rest to 30 m/s in 10 seconds. Calculate the acceleration.
• Initial velocity (u) = 0 m/s (starts from rest)
• Final velocity (v) = 30 m/s
• Time (t) = 10 s
• a = (v – u) ÷ t = (30 – 0) ÷ 10 = 3 m/s²

💡 Study Tips

Positive acceleration = speeding up
Negative acceleration (deceleration) = slowing down
“From rest” means initial velocity = 0
Units: m/s² or km/h²
🎯 Quick Quiz
A ball starts at 5 m/s and reaches 25 m/s in 4 seconds. What is the acceleration?
A) 4 m/s²
B) 5 m/s²
C) 6 m/s²
D) 7.5 m/s²

3 Free Fall

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📖 What is Free Fall?

Free fall occurs when the only force acting on an object is gravity. On Earth, all objects fall with the same acceleration (ignoring air resistance).

🔑 Key Concepts

  • Acceleration due to gravity (g) = 9.8 m/s² (often rounded to 10 m/s²)
  • All objects fall at the same rate (without air resistance)
  • Air resistance opposes motion and slows falling objects
  • Terminal velocity is reached when air resistance = weight

🔢 Free Fall Equations

v = u + gt
Replace ‘a’ with ‘g’ in all acceleration equations
Formula Use
v = u + gt Final velocity after falling
s = ut + ½gt² Distance fallen
v² = u² + 2gs When time is unknown

💡 Study Tips

Use g = 10 m/s² for quick calculations
Replace ‘a’ with ‘g’ in acceleration equations
A feather and hammer fall at the same rate in vacuum
🎯 Quick Quiz
An object is dropped from rest. What is its velocity after 3 seconds? (use g = 10 m/s²)
A) 10 m/s
B) 20 m/s
C) 30 m/s
D) 40 m/s

4 Force and Mass

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📖 Newton’s Second Law

Force = mass × acceleration
F = ma

Forces cause objects to accelerate. The relationship between force, mass, and acceleration is fundamental to understanding motion.

📏 Units

  • Force (F) in Newtons (N)
  • Mass (m) in kilograms (kg)
  • Acceleration (a) in metres per second squared (m/s²)

💡 Worked Example

Problem: Calculate the force needed to accelerate a 500 kg car at 2 m/s².
• Mass (m) = 500 kg
• Acceleration (a) = 2 m/s²
• F = ma = 500 × 2 = 1000 N

💡 Study Tips

Larger mass = more force needed for same acceleration
Rearrange F = ma to find mass: m = F/a
Rearrange to find acceleration: a = F/m
1 Newton is the force needed to accelerate 1 kg at 1 m/s²
🎯 Quick Quiz
A 200 N force is applied to a 50 kg object. What is the acceleration?
A) 2 m/s²
B) 3 m/s²
C) 4 m/s²
D) 5 m/s²

5 Friction

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📖 What is Friction?

Friction is a force that opposes motion between surfaces in contact. It always acts in the opposite direction to movement.

🔑 Key Concepts

  • Friction opposes motion (always acts backward)
  • Friction depends on surfaces in contact
  • Smoother surfaces = less friction
  • Friction converts kinetic energy to heat
  • Useful: brakes, walking, gripping
  • Problematic: machine wear, energy loss

⬇️ Reducing Friction

Methods

  • Lubrication (oil, grease)
  • Streamlining shapes
  • Ball bearings in wheels
  • Polishing surfaces

Types

  • Static friction: prevents starting motion
  • Kinetic friction: opposes moving objects
  • Static > Kinetic (harder to start than continue)

💡 Study Tips

Friction force increases with object weight
Static friction (starting) > kinetic friction (moving)
Without friction, we couldn’t walk or drive!
🎯 Quick Quiz
Which of these does NOT reduce friction?
A) Adding oil between surfaces
B) Using ball bearings
C) Increasing surface roughness
D) Streamlining the shape

6 Gravity

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📖 Understanding Gravity

Gravity is the force of attraction between all objects with mass. On Earth, it gives objects weight and causes them to fall downward.

🔢 Key Formula

Weight = mass × gravitational field strength
W = mg (where g = 10 m/s² on Earth)

⚖️ Mass vs Weight

Mass

  • Amount of matter in object
  • Measured in kilograms (kg)
  • Same everywhere
  • Scalar quantity

Weight

  • Force of gravity on object
  • Measured in Newtons (N)
  • Changes with gravity
  • Vector quantity

💡 Worked Example

Problem: A person has a mass of 60 kg. Calculate their weight on Earth.
• Mass (m) = 60 kg
• Gravitational field strength (g) = 10 m/s²
• Weight = mg = 60 × 10 = 600 N

💡 Study Tips

On Moon: g = 1.6 m/s² (weight is 1/6 of Earth)
Weight always acts downward toward planet center
In space (no gravity), objects are weightless but still have mass
🎯 Quick Quiz
An object has a mass of 80 kg on Earth. What would be its mass on the Moon?
A) 13.3 kg
B) 40 kg
C) 80 kg
D) 480 kg

7 Action and Reaction

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📖 Newton’s Third Law

For every action, there is an equal and opposite reaction
Forces always occur in pairs

🔑 Key Concepts

  • Action and reaction forces are equal in size
  • They act in opposite directions
  • They act on different objects
  • They happen at the same time

🌍 Real-World Examples

Action Reaction
You push on wall Wall pushes back on you
Rocket pushes gas backward Gas pushes rocket forward
Your feet push ground backward Ground pushes you forward
Earth pulls you down You pull Earth up (tiny!)

💡 Study Tips

Action-reaction pairs act on different objects
They never cancel out (different objects!)
Swimming: push water back, water pushes you forward
🎯 Quick Quiz
Why don’t action-reaction force pairs cancel each other out?
A) They have different magnitudes
B) They act on different objects
C) They act at different times
D) They act in the same direction

8 Vectors and Scalars

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📖 Understanding the Difference

Physical quantities can be classified as either vectors or scalars based on whether they have direction.

⚖️ Comparison

Scalar Quantities

Magnitude only (size)

  • Speed
  • Distance
  • Mass
  • Time
  • Temperature
  • Energy

Vector Quantities

Magnitude AND direction

  • Velocity
  • Displacement
  • Force
  • Acceleration
  • Weight
  • Momentum

➕ Vector Addition

When adding vectors, you must consider direction. Vectors in the same direction add; vectors in opposite directions subtract.

Examples:
• 5 N east + 3 N east = 8 N east
• 5 N east + 3 N west = 2 N east

💡 Study Tips

Speed vs Velocity: Speed is “how fast”, velocity is “how fast in what direction”
Distance vs Displacement: Distance is path length, displacement is straight-line distance with direction
Arrows show vectors in diagrams (length = magnitude, arrow = direction)
🎯 Quick Quiz
Which of these is a vector quantity?
A) Temperature
B) Speed
C) Force
D) Mass

9 Circular Motion

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📖 What is Circular Motion?

When an object moves in a circle at constant speed, it is constantly changing direction, which means it is accelerating even though its speed stays the same.

🔑 Key Concepts

  • Centripetal force keeps object moving in circle
  • Always directed toward center of circle
  • Speed constant, but velocity changes (direction changes)
  • Changing velocity = acceleration toward center

🌍 Examples of Circular Motion

Example Centripetal Force
Moon orbiting Earth Gravity
Car turning corner Friction between tires and road
Ball on string swung in circle Tension in string
Satellite orbiting Earth Gravity

⚡ Important Points

  • Without centripetal force, object moves in straight line (Newton’s First Law)
  • Faster speed needs larger centripetal force
  • Smaller radius needs larger centripetal force

💡 Study Tips

Centripetal = “center seeking”
If string breaks, object flies off tangentially (perpendicular to radius)
There is NO “centrifugal force” pushing outward – that’s just inertia!
🎯 Quick Quiz
What provides the centripetal force for a car turning a corner?
A) Gravity
B) Friction
C) Air resistance
D) Engine power