Brief OverviewCircular Motion: In this unit, we focused on centripetal motion, which is the description of an object’s movement around in a circle with a set radius. We first looked at the relationship between angular displacement and circular motion. From there, we learned how to convert the angular velocity of an object to the tangential speed of an object by using the radius. We did this by converting the angular velocity into radians, then multiplying it by the radius. Next, we learned how to determine an object’s centripetal acceleration based on the velocity of the object and its radius. We could then calculate the force of an object moving with centripetal acceleration. Lastly, we worked with the universal force of gravity to help better explain the force of gravity interacting between two objects.
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Uniform Circular MotionUniform Circular Motion can be described as the revolution of an object around a set center, with a radius that stays constant for the duration of the motion of the object. If this stays true, we know the object has a centripetal velocity that can be measured by measuring the time it takes to make a certain number of rotations. We divide the distance (derived from the circumference of the circle) by the time of the rotation to calculate the speed of an object in circular motion. After we have the velocity of the object, we can simply relate the speed of an object to its centripetal acceleration. This is because velocity is simply a measure of speed, so any change in speed or change in direction will result in some sort of acceleration for the object. We can define the relationship between velocity and acceleration as (centripetal acceleration) = (velocity)^2 / (radius). This equation is important, as we can use it to solve for whatever of those three variables we desire. Also, once we have derived the centripetal acceleration, we can multiply it by the mass to get the net force of the object, according to Newton’s second law which states that Net Force = mass times acceleration. We also know that because it is circular motion, there will always be a force pointing towards the center of the circle, as it keeps the object moving in that circular path.
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Universal GravitationUniversal Gravitation can be described as the expression for the force of gravity between two objects. This equation shows the more general relationship between mass, radius, and gravity that we simplify to F=mg on Earth. Universal Gravitation works with the total radius, the mass of each object interacting, and the gravitational constant G (6.67x10^-11). The equation for Universal Gravitation is Fg = ((G)(M1)(M2)) / (R)^2. This equation helps us to better understand the force of gravity interacting with two separate objects. It is dependent on the mass of each object, and the distance between them, or the radius. If the masses of the objects increase, so does the force of gravity. If the radius between the objects increases, then the force of gravity decreases. We can plug in the mass and radius for many different objects here to see what the force of gravity is acting on each object. The gravitational constant, like the name implies, stays the same through our calculations. And because this is often the only force acting on an object, therefore the net force, we can then use it to calculate the acceleration or mass of an object using Newton’s second law.
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