1. What Is Dynamics?

Dynamics is the study of motion and the forces that cause or change that motion.

A force is an interaction that can change an object's velocity, shape, or direction of motion.

Force is a vector quantity, meaning it has both magnitude and direction. The SI unit of force is the newton (N).

The central relationship in Grade 11 dynamics is Newton's Second Law:

This equation tells us that an object's acceleration depends on the net force acting on it and its mass.

2. Newton's First Law of Motion

Newton's First Law is often called the Law of Inertia.

An object at rest remains at rest, and an object moving with constant velocity continues moving with constant velocity unless acted upon by a net external force.

Mathematically, if the net force is zero:

then:

Notice that zero acceleration does not necessarily mean the object is stationary. It can also mean that the object is moving at constant velocity.

Example

A hockey puck sliding across smooth ice can continue moving for a considerable distance because there is relatively little friction.

In everyday life, friction often prevents us from observing perfect constant motion for long periods.

3. Newton's Second Law of Motion

Newton's Second Law describes the relationship between net force, mass and acceleration.

where:

• F_net = net force in newtons (N)
• m = mass in kilograms (kg)
• a = acceleration in m/s²

Therefore:

A larger net force produces greater acceleration for the same mass. A larger mass produces less acceleration for the same net force.

Example

A 10 kg object experiences a net force of 30 N.

Therefore:

4. Newton's Third Law of Motion

Newton's Third Law states that when one object exerts a force on another object, the second object exerts an equal-magnitude force in the opposite direction on the first object.

For example, when you push against a wall, you exert a force on the wall. The wall simultaneously exerts a force of equal magnitude in the opposite direction on you.

A common mistake is thinking that Newton's Third Law forces cancel each other. They do not cancel because they act on different objects.

Action-Reaction Pair

• Same magnitude
• Opposite direction
• Same interaction
• Act on different objects

5. Types of Forces

Grade 11 dynamics problems involve several common forces. Learning how to recognize each force is essential before drawing a free-body diagram.

Gravity

Gravity is the attractive force between masses. Near Earth's surface, the gravitational force on an object is commonly calculated using:

where:

• F_g = gravitational force
• m = mass
• g = gravitational acceleration

Near Earth's surface:

Gravity acts vertically downward.

Normal Force

The normal force is a contact force exerted by a surface on an object. It acts perpendicular to the contact surface.

For an object resting on a horizontal surface with no vertical acceleration:

However, the normal force is not always equal to the object's weight. Inclined surfaces, vertical acceleration and other forces can change its magnitude.

Friction

Friction is a force that opposes relative motion or the tendency of surfaces to move relative to one another.

Two important types are:

• Static friction — acts when surfaces are not sliding relative to each other.
• Kinetic friction — acts when surfaces slide relative to each other.

Kinetic friction can be modelled using:

where \( \mu_k \) is the coefficient of kinetic friction.

Tension

Tension is the pulling force transmitted through a rope, cable, string or similar flexible connector.

Tension acts along the rope or cable, pulling away from the object.

Applied Force

An applied force is a force exerted directly on an object by another object or person.

Examples include pushing a shopping cart, pulling a sled, or pushing a box across a floor.

6. Free-Body Diagrams

A free-body diagram (FBD) is a simplified diagram showing all external forces acting on a selected object.

Free-body diagrams are one of the most useful tools for solving dynamics problems.

How to Draw a Free-Body Diagram

1. Choose the object you are analysing.
2. Represent the object with a simple box or dot.
3. Draw every relevant external force as an arrow.
4. Point each arrow in the correct direction.
5. Label every force.
6. Choose coordinate axes when needed.

For a box resting on a horizontal floor, the basic forces may be:

• Normal force upward
• Gravity downward

If the box is pushed to the right across a rough surface, the diagram may also contain:

• Applied force to the right
• Friction to the left

7. Net Force

When several forces act on an object, we combine them to determine the net force.

In one dimension:

Suppose an object experiences 50 N to the right and 20 N to the left. If right is positive:

The net force is 30 N to the right.

Newton's Second Law can then be applied:

8. Forces on an Inclined Surface

Inclined-plane problems are common applications of Newton's Laws. When an object sits on a slope, it is useful to resolve gravity into components parallel and perpendicular to the slope.

For an incline angle \( \theta \):

The component perpendicular to the slope is:

For a simple situation with no acceleration perpendicular to the surface:

Friction can then be calculated using the normal force.

9. Applications to Circular Motion

Circular motion occurs when an object follows a circular path. Even if the object's speed remains constant, its velocity changes because its direction continuously changes.

Therefore, uniform circular motion involves acceleration.

The acceleration is directed toward the centre of the circular path and is called centripetal acceleration.

where:

• a_c = centripetal acceleration
• v = speed
• r = radius

Applying Newton's Second Law gives the centripetal force:

An important point is that centripetal force is not usually a new type of force. It is the net inward force responsible for circular motion.

Depending on the situation, centripetal force can be provided by tension, friction, gravity, the normal force, or a combination of forces.

10. Work

In physics, work is done when a force causes displacement in the direction of the force.

If a constant force acts in the same direction as the displacement:

More generally:

where \( \theta \) is the angle between the force and displacement.

The SI unit of work is the joule (J).

Positive Work

If force and displacement point in the same direction:

and:

Negative Work

If the force acts opposite to the displacement, the work is negative. Friction commonly does negative work on a moving object.

Zero Work

If the force is perpendicular to displacement:

therefore:

11. Work and Kinetic Energy

Work is closely connected to energy.

The work-energy theorem states that the net work done on an object equals its change in kinetic energy.

Kinetic energy is the energy associated with motion:

Therefore:

If net work is positive, the object's kinetic energy increases. If net work is negative, its kinetic energy decreases.

12. Gravitational Potential Energy

An object can store energy because of its position in a gravitational field.

Near Earth's surface, gravitational potential energy can be calculated using:

where:

• E_g = gravitational potential energy
• m = mass
• g = gravitational acceleration
• h = height relative to the chosen reference level

The choice of zero height is a reference choice. What matters is the change in gravitational potential energy.

13. Conservation of Mechanical Energy

Mechanical energy is the sum of kinetic and potential energy.

When only conservative forces are doing work, mechanical energy remains constant:

For example, as an object falls, gravitational potential energy decreases while kinetic energy increases.

If friction is present, some mechanical energy is transformed into other forms, such as thermal energy.

14. Power

Power describes how quickly work is done or energy is transferred.

Average power is:

where:

• P = power
• W = work
• t = time

The SI unit of power is the watt (W).

If a machine performs the same amount of work in less time, it has greater power.

Power and Force

When a constant force acts in the direction of velocity:

More generally:

15. Worked Example: Newton's Second Law

A 5 kg box is pushed with a net horizontal force of 25 N. Find its acceleration.

Step 1: Identify the values

Step 2: Apply Newton's Second Law

Step 3: Solve for acceleration

16. Worked Example: Friction

A 10 kg box rests on a horizontal surface. The coefficient of kinetic friction is 0.20. Find the kinetic friction force.

Step 1: Find the normal force

For a horizontal surface with no vertical acceleration:

Step 2: Calculate friction

17. Common Dynamics Mistakes

Mistake 1: Confusing Mass and Weight

Mass is measured in kilograms, while weight is a force measured in newtons.

Mistake 2: Drawing Forces That Do Not Exist

Only include actual forces acting on the selected object.

Mistake 3: Forgetting Newton's Third Law Acts on Different Objects

Action-reaction forces do not cancel because they act on different objects.

Mistake 4: Assuming Normal Force Always Equals Weight

This is only true in certain situations, such as an object on a horizontal surface with no vertical acceleration and no additional vertical forces.

Mistake 5: Treating Centripetal Force as a New Force

Centripetal force is the name given to the net inward force responsible for circular motion.

Mistake 6: Forgetting Direction

Force and acceleration are vector quantities. Direction matters.

Mistake 7: Mixing Units

Use SI units whenever possible:

• Mass → kg
• Distance → m
• Time → s
• Force → N
• Energy → J
• Power → W
• Velocity → m/s
• Acceleration → m/s²

18. A Reliable Dynamics Problem-Solving Method

1. Read the problem carefully. Identify what object you are analysing.
2. Draw a diagram. Show surfaces, ropes, slopes, motion and other relevant information.
3. Draw a free-body diagram. Include all relevant external forces.
4. Choose coordinate axes. Select positive directions that make the problem easier.
5. Resolve forces into components when necessary. This is particularly useful for inclined surfaces and two-dimensional problems.
6. Calculate the net force. Add forces using their directions and components.
7. Apply Newton's Second Law.
\[ \vec{F}_{\text{net}}=m\vec{a} \]
8. Check your answer. Make sure the units, direction and magnitude are physically sensible.

19. Grade 11 Dynamics Formula Sheet

20. Quick Revision Checklist

Before your Grade 11 Physics assessment, make sure you can:

• Explain Newton's First Law and inertia.
• Apply Newton's Second Law to force problems.
• Explain Newton's Third Law using force pairs.
• Distinguish mass from weight.
• Calculate gravitational force.
• Identify normal force.
• Calculate kinetic friction.
• Identify tension and applied forces.
• Draw accurate free-body diagrams.
• Calculate net force.
• Resolve forces into components.
• Solve problems involving inclined surfaces.
• Explain centripetal acceleration.
• Calculate centripetal force.
• Explain how real forces provide centripetal force.
• Calculate work.
• Calculate kinetic energy.
• Calculate gravitational potential energy.
• Apply conservation of mechanical energy.
• Use the work-energy theorem.
• Calculate power.
• Use correct SI units.
• Include direction when dealing with vector quantities.