StemUp: OCR A A level Physics 2.3: Nature of quantities

What is meant by a scalar quantity? (1)

A physical quantity that has magnitude only and no direction.

What is meant by a vector quantity? (1)

A physical quantity that has both magnitude and direction.

What is the difference between a scalar and a vector quantity? (2)

- Scalars have magnitude only, while vectors have both magnitude and direction.

- Vectors must be added using vector rules that account for direction, whereas scalars can be added arithmetically.

What are two examples of scalar quantities and their units? (2)

Two of:

- Length (m)

- Speed (m/s)

- Energy (J)

- Time (s)

- Mass (kg)

- Temperature (K)

What are two examples of vector quantities and their units? (2)

Two of:

- Displacement (m)

- Velocity (m/s)

- Acceleration (m/s^2)

- Momentum (kgm/s)

- Force (N)

Why can the magnitude of displacement never be greater than the distance travelled? (2)

- Displacement is the shortest distance between the start and end point of a journey.

- Distance is the total path length travelled, so it can be greater than or equal to displacement, but never less.

How would you find the resultant of two parallel vectors? (1)

Add the magnitudes directly and assign the direction of the vectors.

How would you find the resultant of two antiparallel vectors? (1)

Subtract the smaller magnitude from the larger and assign the direction of the larger vector.

How do you find the resultant of two perpendicular vectors? (2)

- Use Pythagoras' theorem to calculate the resultant magnitude.

- Use trigonometry (eg. arctan) to find the angle of the resultant vector.

How can you use different methods to find the resultant of two vectors at an angle to each other? (3)

- Draw a scale diagram and use a ruler and protractor to measure the resultant.

- Draw a vector triangle and apply Pythagoras and the cosine rule to calculate the resultant.

- Resolve both vectors into components, sum the components, and use Pythagoras and trigonometry to find the final magnitude and direction.

How would you resolve a vector into two perpendicular components? (2)

- If a vector F makes an angle θ with the horizontal, the horizontal component is Fcos(θ)

- The vertical component is Fsin(θ)