Question

why do we say that a particle moving in a circle with uniform speed still has an acceleration derive an expression for this acceleration​

Answer 1

Answer:

An object undergoing uniform circular motion is moving with a constant speed. Nonetheless, it is accelerating due to its change in direction. The direction of the acceleration is inwards. An object moving in uniform circular motion will cover the same linear distance in each second of time (constant speed).

Answer 2

Since acceleration is defined as the rate of change in velocity and velocity being a vector has direction and magnitude both then if it has a constant speed and varying direction which leads to a nonzero acceleration of the motion.

Explanation:

Particle moving with uniform speed in a circular path may have uniform speed but its velocity is not uniform because velocity also comprises of the direction which here keeps changing with the motion.

According to the Newton's first law of motion a body continues to be in state of uniform motion until acted upon by an external force. So here an external force which is centripetal force acts on the body.

Now by the Newton's second law the rate of change in momentum is directly proportional to the force applied.

$F=\frac{d}{dt}.p$

$F=\frac{d}{dt}(mv)$

$F=m.\frac{dv}{dt}$

$F=m.a$

So we have an acceleration acting on the mass due to the centripetal force acting on the body.

Mathematically centripetal force is given as:

$F_C=m.\frac{v^2}{r}$

where:

m = mass of the moving object

v = speed of the object

r = radius of the circular motion

a = acceleration of the object

t = time of taken

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TOPIC: centripetal force

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