Relative Motion Physics – 2nd Six Weeks

Motion: A matter of perspective Albert Einstein once famously said that “imagination is more important than knowledge” When dealing with the topic of Relative Motion and Velocity you will need to use your imagination You will have to imagine what would be seed from different points of view and how moving at different velocities can vary your perspective.

Relative Motion All motion is relative Relative motion is just a way of saying that sometimes different people will say different things about the motion of the same object. This is not because one of them is wrong, but because they are using different frames of reference. The Frame of Reference is something that has been chosen to compare the movement of something against. An object’s motion (or lack thereof) is always established with reference to something else For most of the things we measure, the Earth is the frame of reference

Relative Motion Example : Sitting at your desk, how fast are you moving? Relative to the ground: Zero. You’re not moving relative to the frame of reference of the ground. Relative to the sun: 2.97x104 m/s (approximately 66,500 miles/hour)! That’s a pretty big difference, but since the Earth is orbiting the sun at this speed, an observer standing on the sun (ouch!) would say that you are moving at 2.97x104 m/s. Both of these answers are correct in their own frame of reference. BTW: if it ever comes up on Jeopardy! , you are also moving at 483,000 miles/hour around the center of the galaxy (since the Earth’s creation it has gone through about 20 “galactic years), and about 1,000 miles/hour to the East as the Earth spins on its axis

Relative Motion Galileo Galilei (1564-1642) The scientist & mathematician Galileo Galilei was the first to analyze relative motion from multiple reference points To demonstrate how a moving Earth could be consistent with our everyday experience, Galileo introduced a couple of thought experiments in his 1632 book titled "Dialogues Concerning the Two Chief World Systems.“ One of which has been described as “Galileo’s Ship” Galileo surmised that we on Earth don’t notice the motion of it because we all share the same frame of reference whereas someone from outside would be able to see the effect of rotation just as someone would see an arc of a dropped bag from a ship’s mast from the shore even if ship passengers only saw it drop straight down.

Relative Motion, an airplane, & flipping a coin Q: Why if i flip a coin in an airplane does it go straight up & down, shouldn’t it go backwards since the plane is moving? A: No, since you, the air around you and the coin are moving along with the plane at the same velocity. When you toss the coin in the air, it still has the same forward velocity that you and the air do, matching the plane's forward velocity. As long as the plane moves along with constant velocity, there is no experiment you can do inside that plane to determine whether you're sitting still or moving. Either description of you is equally valid, from different points of view (frames of reference).

Terms and Important Information Speed is the change of position over time and is a scalar quantity (ex: 30 meters/second) Velocity is speed with direction and is a vector quantity (ex: 30 meters/second North) When dealing with movement in 1 dimension, directionality is often given as either being positive or negative. 𝑣 symbolizes velocity so 𝑣 A means “Velocity A” the division symbol “ / “ means “relative to” therefore 𝑣 A/B means “Velocity A relative to Velocity B” or “Velocity A from Velocity B’s Frame of Reference”

Finding Relative Velocity compared to a “Stationary” Reference Point

Finding the Relative Velocity Relative to a Stationary Reference Point – in 1-D: Example #1 . When finding the relative velocity of an object that is on another moving object the velocities are added together (the final velocity is relative to the Earth) The general formula that is used is: 𝑣 𝐴/𝐵= 𝑣 A/C + 𝑣 C/B The formula is read as Velocity of A relative to the Velocity of B is equal to the Velocity of A relative to the Velocity of C plus the Velocity of C relative to the Velocity of B The C’s cancel each other out & we are left with the values at each end (A & B) This process is known as Galilean Velocity Addition

Finding the Relative Velocity compared to a Stationary Reference Point – 1-D: Example #2 . Since velocity is a vector quantity, it is important when adding vector values to be mindful of the sign or direction of each value.

Finding the Relative Velocity compared to a Stationary Reference Point – in 1-D: Example #3 In the first example, the airplane relative to the air was moving at +300 m/s and the wind was moving at -40 m/s relative to the ground so the velocity of the airplane relative to the ground was +260 m/s In the 2nd example, the airplane relative to the air was moving at +300 m/s and the wind was moving at +40 m/s relative to the ground so the velocity of the airplane relative to the ground was +340 m/s

Finding the relative velocity of an object relative to a stationary reference point – 2 D example #1 When dealing with 2 D situations, we add the values using the vector addition method For example 𝑣 person/shore = 𝑣 person/ship + 𝑣 ship/shore 𝑣 person/shore = ( 𝑣 person/ship) 2 + 𝑣 ship/shore 2 𝑣 person/shore = 9+16 = 5 m/s NE Note: without trig functions being used, to find the measure Of the resultant in degrees or when the vectors do not make A right triangle – they will have to be drawn to scale and the Magnitude and direction of the resultant will have to be Measured with a ruler and protractor.

Finding the relative velocity of an object relative to a stationary reference point – 2 D example #2 In this example a man is paddling a boat 5m/s N relative to the river and is being pushed by a river current running 2m/s E relative to the shore 𝑣 boat/shore = 𝑣 boat/river + 𝑣 river/shore 𝑣 boat/shore = ( 𝑣 boat/𝑟𝑖𝑣𝑒𝑟) 2 + 𝑣 river/shore 2 𝑣 boat/shore = 25+4 = 5.4 m/s NE Note: without trig functions being used, to find the measure Of the resultant in degrees or when the vectors do not make A right triangle – they will have to be drawn to scale and the Magnitude and direction of the resultant will have to be Measured with a ruler and protractor.

Finding Relative Velocity compared to another “Moving” Object

Comparing the motion of a moving object to another moving object in 1-D: Example #1 When comparing one moving object’s motion relative to another, we will use subtraction (VA and VB are assumed to be relative to the Earth in the formula) 𝑣 𝐴/𝐵= 𝑣 A - 𝑣 B 40 km/h 50 km/h V A/B = 50 km/h – (-40 km/h) V A/B = 90 km/h Its is as if Car A is approaching at 90 km/h & is an example of why head on collisions are more dangerous

Comparing the motion of a moving object to another moving object in 1-D: Example #2 When comparing one moving object’s motion relative to another, we will use subtraction 𝑣 𝐴/𝐵= 𝑣 A - 𝑣 B 40 km/h 50 km/h V A/B = 50 km/h – (-40 km/h) V A/B = 90 km/h Relative to Car B, Car A is moving away at 90 km/h in a positive direction

Comparing the motion of a moving object to another moving object in 1-D: Example #3 When comparing one moving object’s motion relative to another, we will use subtraction 𝑣 𝐴/𝐵= 𝑣 A - 𝑣 B V Jockey/Runner = -17m/s – (-5m/s) V Jockey/Runner = -12 m/s Relative to the runner, the jockey on the horse is moving ahead of the runner at a velocity of -12m/s

Comparing the motion of a moving object to another moving object – in 2D: Example #1 When comparing one moving object’s motion relative to another, we will use subtraction 𝑣 𝐴/𝐵= 𝑣 A - 𝑣 B Note: subtracting a vector is like adding the inverse of that vector so subtracting out 3m SE is like adding 3m SW, or subtracting out 10 m 135° is like adding 10 m 315° therefore 𝑣 𝐴/𝐵= 𝑣 A + (- 𝑣 B) FYI: ms-1 means the same thing as m/s

Comparing the motion of a moving object to another moving object – in 2D: Example #1 therefore 𝑣 𝐴/𝐵= 𝑣 A + (- 𝑣 B) V Green/Red = V Green – V Red V Green/Red = 35 m/s N + (25 m/s W) V Green/Red = ( 35 2 + 25 2 ) V Green/Red ≈ 43 m/s NW Think about the result and see if it matches your common sense view of how you would see the green car moving if you were in the red car. It would seem to be moving up the page and towards the left. It does actually fit the result!

Comparing the motion of a moving object to another moving object – in 2D: Example #2 therefore 𝑣 𝐴/𝐵= 𝑣 A + (- 𝑣 B) V Red/Blue = V Red – V Blue V Red/Blue = 100 km/hr S + (100 km/hr W) V Red/Blue = ( 100 2 + 100 2 ) V Red/Blue ≈ 141 m/s SW Think about the result and see if it matches your common sense view of how you would see the red car moving if you were in the blue car looking out your rearview mirror. It would seem to be moving down the page and towards the left. It does actually fit the result!