Explain why the motion of a body which is moving with constant speed in a circular path is said to be accelerated ? the minute hand of a clock is 7 cm long . find the displacement and the distance covered by it from 9.00am to 9.30am.

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by yashwanthvps

2015-09-25T21:38:56+05:30

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A body in circular motion has the direction of its velocity along the tangent to the circle at each instant.  As the direction of tangent changes every instant, the vector quantity velocity changes every instant.  No doubt its speed remains a constant.

Since the direction of velocity changes, as per Newtons 1st law, there must be a force to do that.  If we do the vector analysis of velocity at  time  , at time t + Δt , then we find that  vector (v) - vector (v +Δv)  points towards the center of the circle along the radius and has a magnitude  v²/r  Δt.

Thus  dv/dt = acceleration = v² /r .

Thus we say that even in a uniform circular motion,  the object has an acceleration.

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Displacement and distance covered by the point at the tip of the minute hand....

Number of rotations in 30 minutes = 30.  The minute hand comes back to its vertically upward position.  So displacement is 0.  The physical length of the path ie, distance traveled is  30 * 2 π * 7 cm

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