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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.

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.