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How can an object in circular motion be accelerating when it's at the same speed?

In Physics, there are two types of numbers: scalars and vectors. Scalars are just a normal number, as we are used to. Vectors also have a direction associated with them. Thus, variables like temperature and speed are scalars, yet acceleration and weight are vectors.

Because a vector is made up of different parts, one in the x direction, one in the y, if the vector is velocity then these components will change depending on the direction of the object, even if the magnitude of the vector is constant. Because acceleration is the rate of change of the velocity, or the derivative of velocity, this depends upon each component of velocity, thus a change in direction means a change in acceleration.

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