Introduction to Motion, Forces, and Momentum in Physics

- 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 a² + b² = c² 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 = V₂ + (-V₁)

• 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 a² + b² = c² 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 = F₁ + F₂ + F₃ ….+ 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: m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂

• Two objects collide and combine together: m₁u₁ + m₂u₂ = (m₁ + m₂)v

• One object breaks apart into 2 objects in an explosive collision: (m₁ + m₂)u = m₁v₁ + m₂v₂

- 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_netΔt

• or mv - mu

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

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