Unit 1 - Kinematics (review gr.11)

How do you know what to manipulate the X-axis variables by?

You will know what to do with the X-axis values by looking at the relationship between the variable for the Y axis and the var for the X-axis

—> this is shown using the proportional symbol (∝)

How do you find the proportionality relationship in a equation?
(will use this to manipulate vars for curve straightening)

always try to get the physics equation to follow the y = kx format

(move the variable you need)

—> look at picture

What should you remember about

• Best Fit Line

• Calculating the slope of a curve straightened graph?

1. The Line of best fit DOES NOT need to go through the Origin

2. The Line of Best Fit CANNOT have all points above/below the line (aim to have first and last points either above or below)

3. When calculating the slope of a curve straightened line, use values that ARE NOT in your FULL Dataset (y, x, and curve straightened x)

What MUST you remember about vs in physics?

• VS means that any variable on the left is on the Y-axis and the right var is on the X-axis

  (basically Y vs X)

What are 4 steps to find a variable value given an equation and how it was graphed?

1. Look at which vars are on what axis (V vs. √KE)

2. Take your equation and have the Y axis variable by itself on the left (V in this example)

3. Apply any transformations that were done ONLY to the Y-AXIS VARIABLE on the graph (curve straightening)

4. This will give you the slope in the y = kx format and now you can find any variable

When finding x and y components, what are 2 things to remember?

1. clockwise rotation of angle (to the right) = NEGATIVE ANGLE

2. counterclockwise rotation of angle (to the left) = POS ANGLE

(these will be VERY important when having to find vector components)

What are the 2 methods to find the X and Y comps of a vector?

1. Right angle triangle —> (you MUST remember to account for what quadrant you are in and apply + or - to either x or y comps)

2. Std position —> find the corresponding angle but starting on the x-axis

   • you can go either clockwise (- angle) or the other way (+ angle)

What are the 4 acceptable ways to write a answer for a Vector Q?

look at image

What do i and j mean in terms of vectors?

i = x axis components

j = y axis components

(these allow us to group multiple vectors and add them up within brackets)

EX: (1+3+5)i + (-2+3+7)j

EX: for a single vector the notation is: R = (2 m/s)i + (3 m/s)j

• these symbols also need a vector arrow on top of them

(*VERY IMPORTANT*)

In a Vector Q that says “Change in the _____“ what must you remember to do? (Relative Motion)

In a Q that says “Change in velocity/speed/etc…”

—> ALWAYS DO Vector Substraction

The Q will give initial and final vectors so just do (V_f - V_i)

—> This means draw final vector 1st then initial vector

In a vector substraction question, what should you remember for the order of substracting the vectors? (Train Q)

remember that it can be observed object vector - observer’s vector (train Q)

What does “a frame of reference” mean in Relative Motion?

A “frame of reference” means that in any motion problem we need a unit of measurement

(purely horizontal motion can be graphed on a number line)

1. What is the formula for when someone in Object 1 sees Object 2?

2. What must you remember to do with the velocity of the observer object?

3. Car 1 is going right at 80 km/h and Car 2 is going left at 50 km/h. The velocity of 1 seen by 2 is…?

1. ALWAYS remember if 1st sees 2nd we will say “2 seen by 1“

—> V₂₁ = V₂ - V₁

2. We MUST always subtract the observer velocity from the observed velocity

3. its 1 seen by 2 so V₁₂ = V₁ - V₂ = 80 - 50 = 30 km/h right (notice its like they cancel out going diff directions)

What are the 3 steps to Transform a Vector?

1. first calculate the resultant/hyp of the two given components.

2. take this value and multiply the 1/value to the OG components in ij notation

   (we do this because we need to get both components to a magnitude of 1 which is when the resultant/hyp is 1)

3. Now multiply the components in ij notation by the desired magnitude in the question.

what is the formula for finding the resultant for a 3D vector?

r = √r_x² + r_y² + r_z²

What are the 3 types of Vector Multiplication?

• What do they result in? (Scalar or Vector?)

• Give an example for each

1. Scalar Multiplication (Scalar x Vector = Vector)

   • EX: (mass)(accel) = Net Force

2. Vector Dot Product (Vector⋅Vector = Scalar)

   • EX: (force)(displacement) = Work

3. Vector Cross Product (Vector × Vector = Vector)

   • EX: (force)(displacement) = Torque

What is the Definition for:
- Vector Dot Product

• Vector Cross Product

Vector Dot Product: A⋅B = ABcosθ

(A and B are the magnitudes of vectors A and B and θ is the smaller of the 2 angles between A and B when they are joined by their tails)

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Vector Cross Product: A x B = ABsinθ

(same rules as Dot product, only change is now its sine)

What is:

Position?

Displacement?

Avg Velocity?

AVg speed?

avg accel?

Distance?
Instantaneous velocity?

Instataneous speed?

Position (vector) = location of obj on coordinate sys

Displacement (vector) = change of position

Avg Velocity (vector) = displacement over time taken

AVg speed (scalar) = total dist over total time

avg accel (vector) = change in velocity over total time taken

Distance (scalar) = total length of path travelled
Instantaneous velocity (vector) = velocity of obj at a specific time

Instantaneous speed (scalar) = the magnitude of instantaneous velocity (V = √vx2 + vy2) —> New formula 😳

What should you remember about

displacement vs time graphs?

velocity vs time graphs?

in both displacement vs time and velocity vs time graphs:

• slope is decending to x-axis = decel

• neg slope under x-axis = accel in neg direction

What 2 things should you remember about projectiles?

1. The x-comp is CONSTANT —> this means DO NOT use kinematic eqs on the X-comp

2. Remember in many cases you’ll find time it takes for an object to reach the top of the parabola (you’ll need to multiply this by 2 for any total distance calcs)

How do you find the Displacement of a projectile?

(EX: throwing a rock off a cliff)

1. break into x and y comps

2. find each comp with info given (given speed, and asks displacement after certain time, find total dist for each using time given)

3. make new triangle with both and find c² or r² and angle using tan0.

What MUST you REALLY STUDY for this Unit?

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What is the Range Formula, and when can you use it?

Range formula: x = v_i²sin(2θ) / g

• You can only use the range formula when there is no net change in the Y direction (level ground to level ground NOT a cliff Q)