The acceleration of the object moving at a constant speed of 1 revolution per second is 4π²r.
We know that, a body in circular motion possesses centripetal acceleration.
The formula for force according to Newton's second law is F = m * a
The formula for centripetal force is F = (m*v2)/r
By combining both the equations, we can write a = v²/r ---(1)
Given that, constant speed is at the rate of 1 revolution per second.
1 revolution is nothing but the perimeter of the circle which is known as 2π*r.
As the object covers a distance of 2π*r in 1 revolution, its speed is 2π*r m/sec.
From equation (1), Acceleration a = (2π*r)²/r = 4π²r
Thus, the acceleration is 4π²r.
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