| Scalars are physical quantities that have only magnitude (no direction). | Scalars |
| What is a scalar quantity? | A physical quantity that has only magnitude and no direction. |
| Examples of scalar quantities include distance, speed, mass, and temperature. | Examples of Scalars |
| Can you name some scalar quantities? | Distance, speed, mass, and temperature. |
| Vectors are physical quantities that have both magnitude and direction. | Vectors |
| What is a vector quantity? | A physical quantity that has both magnitude and direction. |
| Examples of vector quantities include displacement, velocity, force/weight, and acceleration. | Examples of Vectors |
| Can you name some vector quantities? | Displacement, velocity, force/weight, and acceleration. |
| Two methods to add vectors are calculation (for perpendicular vectors) and graphical (for non-perpendicular vectors). | Methods of Adding Vectors |
| When should you use the calculation method for adding vectors? | When the two vectors are perpendicular to each other. |
| Two forces of 5 N and 12 N acting perpendicular to each other have a resultant force of 13 N using Pythagoras' theorem. | Example of Adding Perpendicular Vectors |
| How do you find the resultant force when two vectors are perpendicular? | Use Pythagoras' theorem: R² =12² + 5² = 169, R = √169 = 13. |
| Use trigonometry to find the direction. For example: tan θ = 5/12, so θ = tan⁻¹ (5/12), = 22.6º | Finding the Direction of the Resultant Vector |
| How do you find the direction of the resultant vector? | Use trigonometry: θ = tan⁻¹ (opposite/adjacent), which gives θ = 22.6º from the horizontal |
| This method is used when vectors are at angles other than 90º. A ruler and protractor are used to draw a scale diagram to find the resultant vector. | Scale Drawing for Vector Addition |
| When should you use a scale drawing to add vectors? | When the vectors are at angles other than 90°. |
| A ship travels 30 m at a bearing of 060° and then 20 m east. Using a scale diagram, the magnitude of displacement is found to be 49 m with a direction of 072°. | Example of Scale Drawing for Vector Addition |
| How do you find the resultant vector using a scale drawing? | Draw the vectors to scale using a ruler and protractor, measure the missing side, and convert the measurement using the scale. |
| Measure the missing angle θ in the scale drawing to find the bearing of the displacement. | Measuring the Direction |
| What tools do you need for adding vectors using a scale drawing? | A ruler and a protractor to draw vectors accurately and measure the resultant magnitude and angle. |
| The opposite of adding vectors. It involves breaking a vector into its perpendicular components, using trigonometry. | Resolving Vectors |
| Why is resolving vectors helpful? | It allows you to analyze perpendicular components separately, as they don’t affect each other. |
| x-component: x = V cosθ y-component: y = V sinθ | Formulas for Resolving Vectors |
| How can you remember when to use cosine or sine while resolving vectors? | If you move through the angle θ to get to the component, use cosine. If you move away from the angle, use sine. |
| A ball is fired at 10 m/s at an angle of 30°. The components of its velocity are: Horizontal: x = 10 cos30° = 8.7 m/s Vertical: y = 10 sin30 | Example of Resolving a Vector |
| The weight of an object on an inclined plane can be broken into two components: parallel to the plane and perpendicular to the plane. | Components of Weight on an Inclined Plane |
| How is the weight of an object on an inclined plane divided? | Into two components: parallel to the plane and perpendicular to the plane. |
| The component of weight parallel to the inclined plane is given by W sin θ, where θ is the angle of inclination. | Parallel Component of Weight |
| How do you calculate the parallel component of weight on an inclined plane? | By using W sin θ, where W is the weight and θ is the angle of inclination. |
| The component of weight perpendicular to the inclined plane is given by W cos θ, where θ is the angle of inclination. | Perpendicular Component of Weight |
| How do you calculate the perpendicular component of weight on an inclined plane? | By using W cos θ, where W is the weight and θ is the angle of inclination. |
| For a block with weight 50 N on a plane inclined at 15°, the parallel component of weight is 50 sin 15° = 12.9 N. | Example - Parallel Component |
| What is the parallel component of weight for a block of 50 N on a plane inclined at 15°? | 12.9 N (calculated as 50 sin 15°). |
| For the same block, the perpendicular component of weight is 50 cos 15° = 48.3 N. | Example - Perpendicular Component |
| What is the perpendicular component of weight for a block of 50 N on a plane inclined at 15°? | 48.3 N (calculated as 50 cos 15°). |
| An object is in equilibrium when the sum of all forces acting on it is zero. This means the object has no resultant force and is either at rest or moving at a constant velocity (Newton's First Law). | Equilibrium |
| What does it mean for an object to be in equilibrium? | It means the sum of all forces acting on the object is zero, and the object is either at rest or moving at a constant velocity. |
| For an object to be in equilibrium, the sum of all forces (both horizontal and vertical components) must equal zero. | Condition for Equilibrium |
| How can you show an object is in equilibrium using force components? | By adding the horizontal and vertical components of all the forces acting on the object and showing that they equal zero. |
| If three forces act on an object in equilibrium, a scale diagram of the forces will form a closed triangle, showing the forces balance. | Three-Force Equilibrium |
| How can you prove an object is in equilibrium if there are three forces acting on it? | By drawing a scale diagram of the forces. If the diagram forms a closed triangle, the object is in equilibrium. |
| Newton's First Law states that an object in equilibrium will remain at rest or continue moving at a constant velocity unless acted upon by a resultant force. | Newton’s First Law and Equilibrium |
| According to Newton's First Law, what happens to an object in equilibrium? | It either remains at rest or moves at a constant velocity. |
