A2 Resource Material

1. MECHANICS
A2: PHYSICAL QUANTITIES, SI UNITS AND VECTORS

2. QUESTION 1: ANSWER C
• Dimensionless quantities occur when the definition of the
quantity under consideration defines a ratio.
• In this case the units of the numerator and the denominator
have the same units.
• As a result when calculations are carried out the units cancel
leaving behind a numerical representation without units.

3. Magnification reference text, reading should be done in preparation for
assessment.

5. Refractive reference text, reading should be done in preparation for
assessment.

6. FURTHERMORE
𝑖
𝑟
𝑖
𝑟
𝑖 𝑟

7. IT IS IMPORTANT TO REMEMBER
Where:
𝑛1 𝑖𝑠 𝑡ℎ𝑒 𝑟𝑒𝑓𝑟𝑎𝑐𝑡𝑖𝑣𝑒 𝑖𝑛𝑑𝑒𝑥 𝑜𝑓 𝑡ℎ𝑒 𝑓𝑖𝑟𝑠𝑡 𝑚𝑒𝑑𝑖𝑢𝑚
𝑛2 𝑖𝑠 𝑡ℎ𝑒 𝑟𝑒𝑓𝑟𝑎𝑐𝑡𝑖𝑣𝑒 𝑖𝑛𝑑𝑒𝑥 𝑜𝑓 𝑡ℎ𝑒 𝑠𝑒𝑐𝑜𝑛𝑑 𝑚𝑒𝑑𝑖𝑢𝑚
1 𝑛2 𝑟𝑒𝑓𝑒𝑟𝑠 𝑡𝑜 𝑙𝑖𝑔ℎ𝑡 𝑚𝑜𝑣𝑖𝑛𝑔 𝑓𝑟𝑜𝑚 𝑡ℎ𝑒 𝑓𝑖𝑟𝑠𝑡 𝑚𝑒𝑑𝑖𝑢𝑚 𝑡𝑜 𝑡ℎ𝑒 𝑠𝑒𝑐𝑜𝑛𝑑

8. Amplitude reference text, reading should be done in preparation for
assessment.

10. Relative Density reference text, reading should be done in
preparation for assessment.

11. QUESTION 2: ANSWER C
• Note quantities can be classified as
• Fundamental: Base quantities are combined using the specific
calculations to form all other quantities.
• Derived: The result obtained when base quantities are
evaluated.

13. QUESTION 3: ANSWER C
• Simply put:
•If a quantity is NOT one of the fundamental
quantities listed it must be a derived quantity.

14. QUESTION 4: ANSWER B
• It is important to remember units of temperature when
referring to an incremental change in the measure of body
degree of “hotness” is just that.
• That is: a 10 degree change in temperature, whether it is in
Celsius ℃, Kelvin 𝐾 or Fahrenheit ℉, is just that. It refers a 10°
change on the scale being used (comparatively speaking).

15. QUESTION 5: ANSWER B
𝐹 = 𝑚 × 𝑎
= 𝑘𝑔 × 𝑚𝑠−2
= 𝑘𝑔𝑚𝑠−2

16. REMEMBER: KNOW THE COMPOSITION OF YOUR DERIVED
QUANTITIES

17. TABLE CONTINUED

18. QUESTION 6: ANSWER C
• 𝐹𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦 =
1
𝑝𝑒𝑟𝑖𝑜𝑑 𝑡𝑖𝑚𝑒 𝑇
𝑡ℎ𝑎𝑡 𝑖𝑚𝑝𝑙𝑖𝑒𝑠 𝑢𝑛𝑖𝑡: 𝑠−1
• 𝑅𝑒𝑠𝑖𝑠𝑡𝑎𝑛𝑐𝑒 =
𝑣𝑜𝑙𝑡𝑎𝑔𝑒
𝑐𝑢𝑟𝑟𝑒𝑛𝑡
𝑡ℎ𝑎𝑡 𝑖𝑚𝑝𝑙𝑖𝑒𝑠 𝑢𝑛𝑖𝑡: 𝑉𝐴−1
• 𝑃𝑜𝑤𝑒𝑟 =
𝑒𝑛𝑒𝑟𝑔𝑦
𝑡𝑖𝑚𝑒
𝑡ℎ𝑎𝑡 𝑖𝑚𝑝𝑙𝑖𝑒𝑠 𝑢𝑛𝑖𝑡: 𝐽𝑠−1
• 𝑃𝑟𝑒𝑠𝑠𝑢𝑟𝑒 =
𝑓𝑜𝑟𝑐𝑒
𝑎𝑟𝑒𝑎
𝑡ℎ𝑎𝑡 𝑖𝑚𝑝𝑙𝑖𝑒𝑠 𝑢𝑛𝑖𝑡: 𝑁𝑚−2

19. QUESTION 7: ANSWER C
• Recall above
• 𝑃𝑜𝑤𝑒𝑟 =
𝑒𝑛𝑒𝑟𝑔𝑦
𝑡𝑖𝑚𝑒
𝑡ℎ𝑎𝑡 𝑖𝑚𝑝𝑙𝑖𝑒𝑠 𝑢𝑛𝑖𝑡: 𝐽𝑠−1
• 𝑡ℎ𝑒 𝑢𝑛𝑖𝑡 𝑓𝑜𝑟 𝑝𝑜𝑤𝑒𝑟 𝐽𝑠−1 𝑏𝑎𝑠𝑒 𝑢𝑛𝑖𝑡𝑠 = 𝑊𝑎𝑡𝑡𝑠 𝑊 (𝑑𝑒𝑟𝑖𝑣𝑒𝑑 𝑢𝑛𝑖𝑡)

20. QUESTION 8: ANSWER A

21. REMEMBER:
• When moving to a bigger unit ×
• When moving to a smaller unit ÷
• Therefore
• 25 × 1000000 =
• 25 × 106 𝑚𝑉

22. QUESTION 9: ANSWER D
• Recall
• Vector quantities have both size and magnitude.

23. CONSIDERING EACH QUANTITY
• Mass (kg)
• Pressure (Pa)
• Frequency (Hz)
• Displacement (m)
Scalar
Scalar
Scalar
Scalar

24. Question 10: answer b

25. QUESTION : ANSWER ?
• Considering the vectors
acting along the y plane:
• This results in:
4
N
1
N
3
N
4 − 1 = 3𝑁

26. • Now considering the vectors
acting along the y plane:
• Resulting in:
3
N
5
N
1
N
3 + − 5 + 1 = −3
The – sign indicates
direction
3
N

27. • We are then left with • Since the vectors act at right
angles to each other:
3
N
3
N
3
N
3
N𝜃

28. AND IT FOLLOWS PYTHAGORAS THEOREM CAN BE USED TO
DETERMINE THE SIZE OF 𝜃
• That is
• 𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒
𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡
= tan 𝜃 ∴
• 𝜃 = tan−1(
3
3
) = 45 𝜃

29. That would then imply that the resultant force
and its resulting acceleration, would be acting
in a north-west direction.
45°

30. QUESTION 12: ANSWER C
Vertical
compone
nt
Horizonta
l
compone
nt

31. QUESTION 13: ANSWER B
The forces act at right angles to each other, therefore we
can use Pythagoras Thm to determine the value of the
resultant.

32. QUESTION 14: ANSWER C

34. QUESTION 15: ANSWER D

35. QUESTION 16: ANSWER B
I will not
be
explainin
g this
question,
we have
repeated
this too
often.