Scalars and Vectors

What are the types of quantites?

• a scalar

• a vector

What are scalars?

quantities that have magnitude but not direction

What are vectors?

quantities that have both magnitude and direction

What is distance?

measure of how far an object has travelled, regardless of direction

What is displacement?

a measure of how far it is between two points in space, including the direction

What is speed?

a measure of the distance travelled by an object per unit time, regardless of the direction

What is velocity?

a measure of the displacement of an object per unit time, including the direction

What are the types of scalars?

Distance, speed, mass, time, energy, volume, density, pressure, electric charge, temperature

What are the types of vectors?

Displacement, velocity, acceleration, force and momentum

How are vectors represented?

• Vectors are represented by an arrow

  • The arrowhead indicates the direction of the vector

  • The length of the arrow represents the magnitude

How can vectors be combined?

• Vectors can be combined by adding them to produce the resultant vector

  • The resultant vector is sometimes known as the ‘net’ vector (eg. the net force)

What are the two methods of adding vectors?

• Calculation – if the vectors are perpendicular

• Scale drawing – if the vectors are not perpendicular

How can the magnitude of a resultant vector be found?

Pythagoras theorem

How can the angle of a resultant vector be found?

Calculating the angle of this resultant vector from the horizontal or vertical can be done using trigonometry

How can a resultant vector be draw and calculated?

• Step 1: Link the vectors head-to-tail if they aren’t already

• Step 2: Draw the resultant vector using the triangle or parallelogram method

• Step 3: Measure the length of the resultant vector using a ruler

• Step 4: Measure the angle of the resultant vector (from North if it is a bearing) using a protractor

What are the parts of a vector?

Horizontal and vertical components

How can two vectors be represented?

a single resultant force

What is the trigonometric function for horizontal component

cos0

What is the trigonometric function for vertical component?

sin0

What is the diagram for object on a inclined plane?

How are coplanar forces represented?

• Coplanar forces can be represented by vector triangles

When are forces in equilibrium?

• Forces are in equilibrium if an object is either

  • At rest

  • Moving at constant velocity

How are coplanar forces represented in equilibrium?

In equilibrium, coplanar forces are represented by closed vector triangles