# Physics Lectures

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## Contents

Physic's lectures presented during 2016 MORT U sessions by Matthew Otey and Brian Holton

## Vectors

Plenty of measurements in physics require both magnitude and direction to be accounted for. These are called vectors, and are represented as arrows.

## Motion

Changes in an object's location or position over a period of time. Several measurements in motion are vectors:

• Displacement (from starting to destination point)
• $d=vt$
• Distance can be measured in feet or meters
• Velocity (speed with direction)
• $v=\frac{d}{t}$
• Velocity can be measure in ft/s or m/s
• Acceleration (how quickly does the velocity change?)
• $a=\frac{v}{t}$
• Acceleration can be measured in $ft/s^2$ or $m/s^2$
There are a few types of motion
Linear (1D, straight line)
Parabolic (2D, including gravity)
Rotational (turning around an axis)
Circular (revolution, not rotation)
Periodic (oscillations, back-and-forth)

## Forces

A mass of any kind requires an unbalanced force in order to change its motion(accelerate)

Forces are vectors that result in the motion of objects when they are unbalanced

Newton's Three Laws of Motion:

1. Inertia: objects will remain in motion or at rest unless an unbalanced force acts on it.
2. $\sum \vec F=ma$
3. For every action, there is an equal and opposite reaction

Inertia is not a force. It is the natural tendency for objects to continue what they are doing

Forces
Applied (direct propulsion or contact)
Tension (pulled)
Friction (resistance)
Normal (surface)
Weight (gravity)

The force of friction depends on the surfaces in contact with each other.

Friction always opposes potential or occurring motion.

## Simple Machines

A machine to make a task easier to perform(?)

• Lever: Inclined plane.
• Wedge
• Screw
• Pulley: Wheel and Axle

$W=\vec F d$

If an object is displaced by some force, when the work is accomplished. This is a vector measured in Joules

## Power

$P=\frac{W}{t}=\vec F v$

## Energy

A requirement in order to accomplish work (Joules)

• Mechanical (kinetic and potential)
• Nuclear
• Thermal (friction)
• Chemical

$KE=\frac{1}{2}mv^2$

## Momentum

$P=mv$

The tendency for an object to continue moving the way it is moving. This is a vector quantity.

Momentum is always conserved in collisions

$m_1 v_1 + m_2 v_2 = m_1 v(\vec F_2) + m_2 v(\vec F_2)$

Elastic collisions → kinetic energy is conserved

$m_1 v_1 + m_2 v_2 = m_1 v(\vec F_2) + m_2 v(\vec F_2)$

Inelastic collisions → ?

## Electricity

The flow of electric charge, particularly electrons, to power circuits and components.

Conductors allow charge to flow. Insulators prevent the flow of charge.

Generally, the electronic components we will be using will abide by Ohm's Law.

$V=IR$
V, Voltage - electrical potential - Volts
I, Current - flow of electricity - Amps
R, Resistance, material preventing flow - Ohms (Ω)

Fuses physically break to prevent overwhelming current from overheating/destroying a circuit.

Circuit breakers trip (turn off) when too much current flows through them

0.07 Amps is enough send the human body into cardiac arrest

## Gear Ratios

Using a CIM motor with a 10-tooth gear and a direct drive configuration, revolutions per second can be calculated by
$5300\frac{rev}{min}*\frac{1 min}{60s}=88\frac{rev}{s}$

With a 4[?]" wheel, inches per revolution can be calculated by

Circumference - $d = 2\pi r$

$88\frac{rev}{s}*25\frac{inch}{rev} = 2200 in.$ or $183 ft = 55m = 55m/s$

Gears connect to gears. Sprockets connect to each other via chain.

The speed of the edge of a spinning object given by the equation $V=\omega r$
Rotational speed is denoted by $\omega$

$V=\omega_1 r_1 = 2r_2$ or $\omega_1 = \frac{r_2}{r_1}*w_2$

The number of teeth on a gear is proportional to the radius

## Torque

$\tau=r \vec F_\perp$
$\tau$ denotes Torque in N-m (Newton Meters)

A force is a push or a pull Torque causes something to rotate As gear speed decreases, torque increases. Torque and speed are inversely proportional

$\vec F = \frac{\tau_1}{r_1} = \frac{\tau_2}{r_2}$

$\tau_1 = \frac{r_1}{r_2} * \tau_2$

## Center of Mass

Center of Mass for an arm is $\frac{r}{2}$

## Pneumatics

$Pressure = \frac{Force}{Area}$

$Area = \pi r^2$