Bennett Science Blog

Credit: Public Domain By Andrew Bennett What Is Periodic Motion? Simple harmonic motion is a special type of repeating motion motion motion motion (sorry, I couldn't resist). Motion that repeats after a certain amount of time is called periodic motion, where the "period" means the amount of time it takes for the motion to repeat. Simple Harmonic Motion: A Type of Periodic Motion Simple harmonic motion is periodic motion that is caused by a restoring force that is proportional to the object's distance from its equilibrium position. Let's unpack that! SHM Examples The most common examples of objects that undergo simple harmonic motion are a pendulum and a mass vibrating on the end of a spring. It turns out that atoms bonded to other atoms also undergo this type of motion. So, studying a pendulum helps us understand atomic motion and interactions. We know that equilibrium is the state in which all the forces and torques on an object are balanced, so tha

Credit: Public Domain By Andrew Bennett Early on in a first-year physics class, we learn that equilibrium is a state in which an object experiences no net force. As a result, that object does not accelerate. What Is Rotational Equilibrium? It turns out that this definition for equilibrium is not complete. It works well when the location of the force doesn't matter, which occurs when the object will not be rotating. Including the possibility for rotation adds another requirement for equilibrium. Instead of just having no linear acceleration, we must also have no angular (or rotational) acceleration. To achieve this, the net torque on an object must also be zero. For example, if you placed a stick on the ground, then pushed on it equally with your hands in two opposite directions, the stick might not stay still. If your hands are at the same location on the stick, it will remain still. But if your hands are at different locations, the stick will begin to rotate when you push

By Brews ohare [CC BY-SA 3.0 (https://creativecommons.org/licenses/by-sa/3.0) or GFDL (http://www.gnu.org/copyleft/fdl.html)], from Wikimedia Commons By Andrew Bennett The motion of an object going around in circles is of special interest in AP physics 1. From a ball on a string to GPS satellites to charged particles moving through magnetic fields, examples of circular motion are everywhere! Uniform Circular Motion Explained Circular motion with a constant speed is called uniform circular motion. It is a frequent setup for intro-level high school physics classes. Since the speed is unchanging, many will incorrectly assume that the object is not accelerating. In fact, acceleration is a change in an object's velocity, which includes both speed and direction. The speed is constant, but the direction is not. Objects traveling in a circle at a constant speed are always accelerating toward the center of the circle. (We call this centripetal acceleration.) They also have a veloci

Credit: Public Domain By Andrew Bennett Collisions between objects are often treated using the conservation of momentum in physics . Energy can be tricky to deal with. We frequently have some amount of mechanical energy turning to nonmechanical energy, and it's difficult to predict how much. The collision causes atoms within the objects to shake, meaning they have kinetic energy (but we call it thermal energy when it's for individual atoms). This has taken away from the kinetic energy of the objects as a whole. It is not always clear how much of the original kinetic energy the objects will have after the collision. There is no such concern with momentum , so it is a useful way to understand these situations. Classes of Collisions However, we need to know about a few classes of collisions . The classes are divided up according to what is happening with energy in a particular situation. The classes are called elastic collisions, inelastic collisions, and completely (or t

Credit: Public Domain By Andrew Bennett Conservation of Momentum Definition The conservation of momentum is enormously useful, particularly for learning about collisions between objects. Mostly used to describe the collisions of two or more objects, this physics principle means that the total momentum does not change in a closed system. In other words, the total value of momentum is constant when there are no external forces acting on a group of objects. Conservation of Momentum Equation Typically, we use an equation that comes from a special case of the Impulse-Momentum Theorem : When the force on the system is zero, the total momentum does not change. So, we can write an equation stating that the initial total momentum is equal to the final total momentum. This equation can be expanded by including momentum terms for each object. For example, if we have two objects labeled A and B , respectively, we might write this as: . We could also substitute the eq

Credit: Public Domain By Andrew Bennett The momentum of an object is the product of its mass and its velocity. A force must act on an object to change its momentum. The size of the force and the time over which that force acts both determine how much the momentum changes. In fact, the product of the force and the time are exactly equal to the change in momentum of the object. This product is called the " impulse delivered by the force ." Impulse-Momentum Theorem and Newton's Second Law Newton's 2nd Law Definition Newton's 2nd law says that the acceleration of an object ( a ) is equal to the force on it ( F ) divided by its mass ( m ), or: . The acceleration of the object can be calculated as the change in its velocity over the change in time, so we can replace acceleration in the equation above and get: . Multiplying both sides by mass and by time gives the result: . With the product of mass and velocity in that equation, it begin

Credit: Public Domain By Andrew Bennett Linear Momentum Vector Definition and Equation Linear momentum is a vector quantity , meaning it has both magnitude and direction. Before AP Physics 1, we often ignore the direction part. Momentum is the product of an object's mass and velocity. You can write this equation as  p=mv ,  where p is momentum, m is mass, and v is velocity. The direction of the momentum vector will be the same as the direction of the velocity vector. This gets tricky when we have multiple momentum vectors to consider. For example, some more advanced problems consider the momenta of multiple objects at two different moments in time, and you must add those momentum vectors together. Video: How to Solve Basic Linear Momentum Practice Problems This video stresses the importance of thinking of momentum as a vector. It also walks you through an example problem in which we find the total momentum of a system, which requires some vector addit

Credit: Public Domain By Andrew Bennett What Does Power Mean in Physics? The word "power" is used to mean energy and electricity outside of physics. In physics, however, power is specifically the rate at which energy changes. This could be a transfer of energy from one object to another (for example, though work being done). It could also be a change from one type of energy to another (for example, chemical energy turning to kinetic energy). Regardless, power describes how rapidly that change takes place. Since power deals with energy and work, there are a number of different connections you can make with power. Power Equations Power is a rate. All rate measurements are calculated in a similar way: the change in some quantity divided by the amount of time it takes for that change to happen. With power being the rate at which energy changes, we can write the equation for power as: . We also frequently deal with work in introductory physics classes (see my post

Credit: Public Domain By Andrew Bennett Energy Conservation in the Real World We learn early in physics about the Law of Conservation of Energy. Check out my previous post on the topic for a quick refresher on its definition and equations . We also solve a lot of problems that ignore things like friction and air resistance, so our sleds keep sliding and our pendulums keep swinging. Imaginary objects seem to follow the Law of Conservation of Energy quite nicely. However, what about real objects? When we observe the world around us, we see things slow and stop. A car driving on a flat road can't keep the same speed without more energy from gasoline, diesel, etc. Balls don't bounce as high the second time. A child on a swing slows down without being pushed or pumping their legs. Do these examples violate the Law of Conservation of Energy? Of course not! Mechanical and Nonmechanical Energy Video In this video, we review various energy types. Mechanical energy usually

Credit: U.S. Air Force illustration By Andrew Bennett What Is Potential Energy? Potential energy (sometimes called "stored energy") is the energy associated with the positions of objects. These objects also exert forces on one another, and they tend to move toward certain arrangements. What Is Gravity? Gravity is an attractive force (attractive = pulls together rather than pushes apart) that exists between any pair of objects. The amount of gravity depends on the mass of each object and the distance between them. Since the force between "small" objects like you and me is so small, we usually only bother with pairs of objects that include a planet, moon, star, black hole, or some other large celestial object. Gravitational Potential Energy Definition Gravitational potential energy (GPE) is the energy of objects attracting each other via a gravitational force. Although all objects do this, we will most commonly care about the interaction of large obj

Credit: Creative Commons Photo By Andrew Bennett How Do We Use Springs in Physics? One of the common objects we examine in physics is a spring. One of the interesting properties of a spring is the resting length, also called the equilibrium length. When you stretch or compress the spring from the resting length, it stores energy and exerts a force. What Is Hooke's Law? The amount of force that a spring pushes or pulls with depends on how far you stretch or compress the spring. The more you stretch or compress the spring, the more force it exerts. In fact, there is a linear relationship between the stretch or compression length and the force exerted by the spring. This relationship is described by Hooke's Law . The law is commonly rewritten as: The coefficient that relates the stretch or compression length ( x ) to the force ( F ) on the spring is called the spring constant (or sometimes the force constant). It is written as k . How Do We Calculate Spring Poten

YouTube Screenshot (https://www.youtube.com/watch?v=7r4ZS-LYzGs) By Andrew Bennett Work is a tricky term to define because it reaches into considerations of both forces and energy. It is also a quantity that might be easier to understand through equations than word-based definitions. Definition of Work in Words Often, we say that work is the transfer of energy from one system to another by applying a force over some distance. Then, of course, we have to understand energy to understand work. Since we often define energy as the ability to do work, we end up with a somewhat circular definition. What we should recognize right away, though, is that work involves both forces and energy. So, it can sometimes be used as a bridge between two ways of thinking about a scenario. Equations for Work Involving Forces On the forces side of things, we define work as the dot product of the displacement vector (r) and the force vector (F), or: A dot product is one way to multiply two v