# Introduction to Motion, Forces, and Momentum in Physics

Classified in Physics

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## - Scalars and Vectors

• **Scalars** require magnitude and unit (distance, time, speed, mass)

• **Vectors** require magnitude, unit, AND direction (displacement, velocity, acceleration, force)

• Force vectors are drawn with their tails attached to the point of application on the object.

• 1D vectors use right/left, up/down, +/-

• 2D vectors described using angles, measured clockwise and anticlockwise from the vertical and horizontal

## - Adding Vectors

• 1D vector: make one direction (up, right) a positive value and the opposite direction (down, left) a negative value, then add them all up.

• 2D vector: draw the first vector in the appropriate direction, then the second vector from the head of the first. Then use a^{2} + b^{2} = c^{2} to find the hypotenuse of the triangle. This becomes the magnitude for the vector answer. Then use trigonometry to get the angle which becomes the direction for the answer vector.

## - Subtracting Vectors

• 1D: Δ_{vector} = V_{2} + (-V_{1})

• 2D: draw the final vector first, then draw the initial vector (but in the opposite direction) head to tail with the final vector. Draw the resultant vector (hypotenuse) then use a^{2} + b^{2} = c^{2} to find the magnitude for the change in velocity. Then use trigonometry to get the angle which becomes the direction for the answer vector.

## - Mass and Weight

• **Mass** of an object is its ability to resist changes in motion. It is a scalar and is not influenced by external environmental factors. Measured in kilograms.

• **Gravity** is a force of attraction between masses that extends through space.

• **Weight** is a force due to gravity, it is a vector. Measured in Newtons.

## - Displacement, Speed, and Velocity

• **Position** defines the location of an object with respect to a defined origin.

• **Distance travelled**, d, tells us how far the object has actually travelled (scalar).

• **Displacement**, s, is the change in position of an object in a given direction (vector). s = final position - initial position.

• The **average speed** of a body, v_{av}, is the rate of change of distance (scalar) v_{av} = distance / time.

• The **average velocity** of an object is the rate of change of displacement (vector) v_{av} = displacement / time.

• m s^{-1} km h^{-1} = × 3.6

• km h^{-1} m s^{-1} = ÷ 3.6

• Speed and velocity are both measured in m s^{-1}

## - Acceleration

• Change in speed (scalar): Δv = v_{speed} - u_{speed}

• Change in velocity (vector): Δv = v - u

• **Acceleration** (vector) is measured in m s^{-2}. a = Δv / Δt or a = (v-u) / Δt

## - Graphing Position, Velocity, and Acceleration Over Time

• Position-time graph: gradient = velocity. If curved, the tangent of any point gives the instantaneous velocity.

• Velocity-time graph: gradient = acceleration. Displacement = area underneath.

• Acceleration-time graph: area underneath = velocity.

## - Equations for Uniform Acceleration

• S = displacement (m)

• U = initial velocity (m s^{-1})

• V = final velocity (m s^{-1})

• A = acceleration (m s^{-2})

• T = time (s)

## - Vertical Motion

• If air resistance is ignored, all bodies falling freely near Earth will move with the same constant acceleration.

• **Acceleration due to gravity**, g, is equal to 9.8 m s^{-2} in the direction towards the center of the Earth.

## 10.3 - Newton's Laws

• A **force** is a push or a pull, some act on contact, others act at a distance.

• Force (N) is a vector.

• **1 ^{st} Law**: An object will continue with its velocity unless an unbalanced external force causes the velocity to change. Net forces cause acceleration.

• F_{net} = F_{1} + F_{2} + F_{3} ….+ F_{n}

• **Inertia** is the tendency of an object to resist changes in motion. Related to mass; large mass means large inertia.

• **2 ^{nd} Law**: the acceleration of an object is directly proportional to the net force on the object and inversely proportional to its mass.

• **Air resistance** is a force that acts to decrease the acceleration of objects through the air.

• **3 ^{rd} Law**: for every action (force) there is an equal and opposite reaction (force).

• If the action force is labelled systematically, the reaction force can be described by reversing the label of the action force.

• The action and reaction forces are equal and opposite even when the masses of the colliding objects are different.

• The individual forces making up the 3^{rd} law pair act on different masses to cause different accelerations according to the 2^{nd} law.

## - Momentum and Conservation of Momentum

• **Momentum**, p, is the product of an object's mass and velocity (vector): p = mv

• Two objects collide and remain separate: m_{1}u_{1} + m_{2}u_{2} = m_{1}v_{1} + m_{2}v_{2}

• Two objects collide and combine together: m_{1}u_{1} + m_{2}u_{2} = (m_{1} + m_{2})v

• One object breaks apart into 2 objects in an explosive collision: (m_{1} + m_{2})u = m_{1}v_{1} + m_{2}v_{2}

## - Momentum Transfer

• Change or transfer in momentum, Δp, is also known as **impulse**, I (vector). Impulse is measured in kg m s^{-1}.

• Impulse occurs when an object changes its velocity.

• I = F_{net}Δt

• or mv - mu

• Impulse in 2D: I = F_{net}Δt or, I = mv - mu, or can be calculated by doing the same as subtracting vectors in 2D.

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