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If an object of mass 4 kg is moving in a circular path of radius 1.5 m with a constant angular velocity of 6 rad/s, what is the centripetal force acting on the object?
If an object of mass 4 kg is moving in a circular path of radius 1.5 m with a constant angular velocity of 6 rad/s, what is the centripetal force acting on the object?
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The centripetal force acting on an object moving in a circular path can be calculated using the formula:
F = m * v^2 / r
Where: F = centripetal force m = mass of the object (4 kg) v = tangential velocity of the object r = radius of the circular path (1.5 m)
First, we need to calculate the tangential velocity of the object using the formula:
v = r * ω
Where: v = tangential velocity r = radius of the circular path (1.5 m) ω = angular velocity (6 rad/s)
v = 1.5 m * 6 rad/s v = 9 m/s
Now, we can substitute the values into the centripetal force formula:
F = 4 kg * (9 m/s)^2 / 1.5 m F = 4 kg * 81 m^2/s^2 / 1.5 m F = 324 N
Therefore, the centripetal force acting on the object is 324 N.