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?

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.