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π‘ΒAP Physics 1

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πUnit 3

2 min readβ’june 8, 2020

Peter Apps

A vector field gives, as a function of position (and perhaps time), the value of a physical quantity that is described by a vector.

Image courtesy of Open University.

As shown in the image above, a vector field can represent circular motion.Β From this vector field depiction, we can go into more depth of the specific components of **uniform circular motion**.

Image courtesy of Quizlet.

From this diagram, we can see in uniform circular motion centripetal acceleration is constant and always **pointed towards the center**, or center-seeking. Similarly, the centripetal force always **points towards the center**. However, velocity is **tangent from the center**; therefore, it is not considered in the net force. All forces pointing towards the center of the circle are positive (+) and all forces pointing away from the center of the circle are negative (-). Anything that doesnβt point away from or towards the circleβs center isnβt considered in the net force.

*Key Concept:***Centrifugal**- moving or tending to move away from a center.*Key Concept:***Centripetal**- moving or tending to move toward a center.*Key Concept:***Centripetal Force**- a force that acts on a body moving in a circular path and is directed toward the center around which the body is moving.

A common misconception with centripetal force is that it is a new force when, in actuality, it is the **net force** inward and should be treated as such. To prove this concept, letβs dive into how the equation for centripetal force is derived: Newtonβs second law gives us the equation *F =ma*, which can also be adapted for net force. Acceleration in a uniform circular motion is given as *a = v^2/r*, so Centripetal Force is simply *mass x v^2/r* or mv^2/r. Remember to **not include centripetal force** on any free-body diagrams because it is not a force, but rather the net force.

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