A rider on a mountain bike is traveling to the left in Figure 8.18. Each wheel has an angular velocity of 21.7 rad/s, where, as usual, the plus sign indicates that the wheel is rotating in the counterclockwise direction. (a) To pass another cyclist, the rider pumps harder, and the angular velocity of the wheels increases from 21.7 to 28.5 rad/s in a time of 3.50 s. (b) After passing the cyclist, the rider begins to coast, and the angular velocity of the wheels decreases from 28.5 to 15.3 rad/s in a time of 10.7 s. In both instances, determine the magnitude and direction of the angular acceleration (assumed constant) of the wheels.
PHYS Notes Week 7 Feb 2226 Electric Charge Particles have either a positive or negative charge Combining these particles into atoms/molecules result in three possibilities Negatively charged: object contains more negative particles than positive particles Positively charged: object contains more positive particles than negative particles Electrically neutral: object contains equal amounts of positive and negative particles Nature prefers neutral charges The terms "positive" and "negative" don't mean anything; they just refer to the fact that the charges are opposite Electrostatic/electric force: the force that charged particles exert on each other Objects with the same electrical charge repel each other, while objects with opposite electrical charges attract each other Strong electrical charges can induce an opposite charge in a neutrally charged system Grounding it can neutralize a system’s charge Grounding: touching an object to the ground (the earth is so big that it can absorb any extra charge without problem) Unit of electric charge is a coulomb (C) Derived from base unit of ampere, which is a measure of current Current: rate at which charge moves past a given point in a given amount of time Charge is quantized (comes in basic units based on electrons that cannot be divided) Basic unit of charge: electron Historically led to the development of quantum mechanics Charge is conserved (cannot be created or destroyed, only moved around) Charge moving through materials Conductors vs. insulators Conductors allow electrons to move freely (ex. metal) Everything can be a conductor with enough electricity Insulators don't allow electrons to move as freely Semiconductors are somewhere in between Superconductors allow charge to move without hindrance Coulomb’s law Force exerted by charged particles on each other depends on the size of the charge of the particles as well as their distance from one another Two positive or two negative charges > particles push away from each other; one negative and one positive charge > particles attract each other * Increasing force means opposite charges (attracting particles) Electric fields: electrostatic forces existing around a charged particle Determine what a field looks like by placing a test charge near it and measuring the force applied to the test charge We draw electric field using field lines Field lines closer together shows stronger force Field lines extend away from positive charges and toward negative charges If we create a field, we can direct a particle through it (old TVs) Charged particles have potential energy Electric potential (voltage): potential energy per electrical charge Electric current: flow of electrons in motion (negative to positive) Produced by voltage Inserting battery into loop of conductive material creates a flow Conduction Some materials conduct electricity better due to resistance of the material Resistance inhibits flow Ohm: unit of resistance Ohm's law: as potential increases, current increases, and when resistance increases, current decreases Series Circuits Battery/power supply: creates a difference in potential energy Path from one end of battery to another (wire or other conductive material) > electrical current Electrons pushed through a resistor, which slows the current down/steals kinetic energy from the electrons to power a machine Power multiple machines by adding multiple resistors to circuit around the circuit Each resistor increases the overall resistance of circuit Parallel circuits Put resistors into a circuit next to each other, creating multiple paths for the electron to move through If one of the paths slows down (because electrons have to slow to enter the resistor), the backedup electrons move through the next parallel resistor Adding resistors decreases the resistance of the circuit, increasing current flow (like adding lanes to a highway) Too fast of a current is an issue because wires can only hold so much electricity Direct current (DC): current that flows in only one direction Usually used in electronics/devices Alternating current (AC): current alternates direction (60 times/s (60 Hz)), which changes, faster than what we can see (20 Hz) Easier to generate and travel over long distances Argument between Tesla (AC) vs. Edison (DC) because AC is dangerous Edison created the electric chair, which used AC Transformers are used to change between AC and DC