1.4 Reference Frames and Relative Motion

• Why do different reference frames provide different perspectives on motion?

  They have different origins
• Match the reference frame with its description:

  1️⃣ Stationary Ground

  2️⃣ A specific point on the ground with orthogonal axes

  3️⃣ Moving Car

  4️⃣ The center of the car with axes parallel to its movement
• A reference frame is a coordinate system used to specify the position and motion of an object.
• From the train's reference frame, a passenger's velocity is their walking speed.


  True
• An inertial reference frame moves at a constant velocity and does not accelerate or rotate.
• Match the type of reference frame with its characteristic:

  Inertial Frame ↔️ Zero acceleration

  Non-Inertial Frame ↔️ Requires fictitious forces
• How is relative velocity calculated?

  By vector addition
• Match the reference frame with the corresponding relative velocity:

  Ground ↔️ 22 m/s east

  Train ↔️ 2 m/s east
• What is the 'Velocity in Frame 1' in the relative velocity formula?

  Object's velocity in its original frame
• Velocity in Frame 1 refers to the velocity of the object as measured in its original reference frame
• Why is relative velocity an important concept in understanding motion?

  Describes motion from multiple perspectives
• The motion of an object appears the same regardless of the reference frame used.

  False
• The choice of reference frame affects the measured velocity of an object.


  True
• Newton's laws hold true in non-inertial reference frames without modifications.

  False
• If a person walks at 2 m/s east inside a train moving at 20 m/s east, what is their relative velocity from the ground's perspective?

  22 m/s east
• What is the formula for calculating the relative velocity of object A with respect to object B?

  $V_{AB} =$$V_{A} - V_{B}$
• What is the formula for relative velocity?

  $V_{AB} =$$V_{A} - V_{B}$
• The velocity of object A is denoted as $V_{A}$


  True
• What is the relative velocity of car X (25 m/s east) with respect to car Y (15 m/s east)?

  10 m/s east
• Steps to solve relative velocity problems

  1️⃣ Identify the two relevant reference frames

  2️⃣ Determine the velocities of the objects in each reference frame

  3️⃣ Apply the relative velocity formula
• If a person walks at 2 m/s east inside a train moving at 20 m/s east, what is the person's velocity from the ground's perspective?

  22 m/s east
• The same motion can appear very different depending on the observer's perspective.


  True
• In the airplane scenario, relative motion accounts for wind speed to optimize flight path and speed.
• A person walks east at 1.5 m/s inside a train moving east at 15 m/s. What is the person's velocity from the ground's perspective?

  16.5 m/s
• Newton's laws always hold in non-inertial reference frames without modification.

  False
• Objects in an inertial reference frame obey Newton's first law, also known as the law of inertia.
• A person walking east in a train moving east has a higher relative velocity from the ground's reference frame than from the train's reference frame.


  True
• The formula for relative velocity is: Relative velocity = Velocity in Frame 1 + Velocity of Frame 1 relative to Frame 2.
• From the train's reference frame, a person walking inside has a relative velocity equal to their walking speed.


  True
• The velocity of Frame 1 relative to Frame 2 is measured from the perspective of Frame 2.


  True
• A reference frame is a coordinate system used to specify the position and motion of an object
• What are the origin and axes of a stationary ground reference frame?

  Specific point on the ground; Orthogonal axes
• An inertial reference frame moves at a constant velocity and does not experience acceleration
• What fictitious force is introduced in non-inertial reference frames to account for acceleration?

  Centrifugal force
• Relative velocity is calculated using vector addition
• Relative velocity allows us to describe the same motion from multiple perspectives.

  True
• The relative velocity of car X with respect to car Y is 10 m/s to the east
• The relative velocity of object A with respect to object B is denoted as V_{AB}</latex>
• The velocity of object B is denoted as $V_{B}$
• When viewed from car Y, car X appears to be moving faster