Uniform speed and velocity, acceleration concept in circular path
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Originally Answered: If a body moves in a circular path with uniform speed, is that body accelerating?
The definition of acceleration is the rate of change of VELOCITY so we need to consider the direction of motion as well as the magnitude of the velocity.
As an object travels in a circular path, it is constantly changing direction. This means that the velocity is changing (if you resolve vertically and horizontally you will see this). If velocity is constantly changing, this must mean that the object in uniform circular motion is accelerating.
But is the acceleration constant?
The force acting on the object in uniform circular motion is not constant but its magnitude is and is and equal to
mv²r
(This only need the magnitude of the velocity, the direction is not important as the velocity is squared)
If we assume that the mass is constant:
a=F/m=mv²r/m
a=v²r
As the velocity is squared, the direction has no effect so this number will always be constant as the magnitude of velocity remains the same throughout, therefore the magnitude of the acceleration is constant in uniform circular motion.
The definition of acceleration is the rate of change of VELOCITY so we need to consider the direction of motion as well as the magnitude of the velocity.
As an object travels in a circular path, it is constantly changing direction. This means that the velocity is changing (if you resolve vertically and horizontally you will see this). If velocity is constantly changing, this must mean that the object in uniform circular motion is accelerating.
But is the acceleration constant?
The force acting on the object in uniform circular motion is not constant but its magnitude is and is and equal to
mv²r
(This only need the magnitude of the velocity, the direction is not important as the velocity is squared)
If we assume that the mass is constant:
a=F/m=mv²r/m
a=v²r
As the velocity is squared, the direction has no effect so this number will always be constant as the magnitude of velocity remains the same throughout, therefore the magnitude of the acceleration is constant in uniform circular motion.
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