3.17 P: Quantities and Units in Mechanics

• Vector quantities have both magnitude and direction.


  True
• The fundamental SI unit for length is the meter
• Order the following derived units from simplest to most complex in terms of derivation:

  1️⃣ Velocity

  2️⃣ Acceleration

  3️⃣ Force

  4️⃣ Energy

  5️⃣ Power
• What are physical quantities used to describe in mechanics?

  The state of a system
• What property distinguishes scalar quantities from vector quantities?

  Direction
• The fundamental SI units form the basis for measuring all other physical quantities in mechanics and science
• Scalar quantities are quantities that have only magnitude
• Match the fundamental SI unit with its symbol:

  Meter ↔️ m

  Kilogram ↔️ kg

  Second ↔️ s
• Velocity is derived from length and time.


  True
• Scalar quantities have both magnitude and direction

  False
• Scalar quantities can have direction

  False
• Derived units are calculated from fundamental SI units


  True
• Unit prefixes modify standard units by factors of 10


  True
• To convert units within the SI system, you always multiply by 10

  False
• The fundamental SI units used in mechanics are used to measure various physical quantities
• Derived units in mechanics are calculated from the fundamental SI units
• Unit prefixes modify standard units by factors of 10.

  True
• Using unit prefixes helps simplify complex numerical values and improves clarity.


  True
• What ensures accurate conversions between different SI units?

  Referring to multipliers
• If the dimensions in an equation do not match, there is a dimensional error
• One kilometer is equal to 1000 meters
• 3.2 micrograms is equal to 0.0000032 grams
• What do the fundamental SI units form the basis for in mechanics and science?

  Measuring other physical quantities
• What is the purpose of derived units in mechanics?

  To quantify physical phenomena
• One kilometer is equal to 1000 meters.
• To convert 5 kilometers to meters, you multiply by 1000
• Steps in applying dimensional analysis:

  1️⃣ Identify the dimensions of each term

  2️⃣ Check the dimensional consistency of the equation

  3️⃣ Identify any dimensional errors
• The fundamental SI unit for thermodynamic temperature is the kelvin
• Match the quantity with its derived unit:

  Acceleration ↔️ m/s²

  Force ↔️ N

  Power ↔️ W
• Vector quantities have both magnitude and direction
• What are examples of scalar quantities?

  Mass, time, speed
• Force is measured in Newtons
• Match the unit prefixes with their multipliers:

  kilo ↔️ 10^3

  mega ↔️ 10^6

  giga ↔️ 10^9

  milli ↔️ 10^-3

  micro ↔️ 10^-6

  nano ↔️ 10^-9
• How many meters are in 5 kilometers?

  5000
• Match the physical quantity with its fundamental SI unit and symbol:

  Length ↔️ Meter (m)

  Mass ↔️ Kilogram (kg)

  Time ↔️ Second (s)

  Electric current ↔️ Ampere (A)

  Thermodynamic temperature ↔️ Kelvin (K)

  Amount of substance ↔️ Mole (mol)

  Luminous intensity ↔️ Candela (cd)
• Match the derived quantity with its derived unit and derivation:

  Velocity ↔️ m/s (m and s)

  Acceleration ↔️ m/s² (m and s)

  Force ↔️ N (kg, m, and s)

  Energy ↔️ J (kg, m, and s)

  Power ↔️ W (J and s)
• Match the prefix with its symbol and multiplier:

  kilo ↔️ k (10^3)

  mega ↔️ M (10^6)

  giga ↔️ G (10^9)

  milli ↔️ m (10^-3)

  micro ↔️ μ (10^-6)

  nano ↔️ n (10^-9)
• Steps to convert units within the SI system:

  1️⃣ Identify the prefixes of the units

  2️⃣ Refer to the multipliers of the prefixes

  3️⃣ Multiply or divide by the appropriate power of 10
• Dimensional analysis checks if an equation is dimensionally consistent.


  True