If the ladybug has a mass of 6.0 kg and is at a distance r = 1 m, find her A) velocity, B) centripetal acceleration, and C) centripetal force.

a) 3.14 m/s

b)

c) 59.4 N

Explanation:

a)

The relationship between angular velocity and linear velocity for an object in circular motion is given by:

where

is the angular velocity

v is the linear velocity

r is the distance between the object and the axis of rotation

For the ladybug in this problem, we have:

r = 1 m (distance)

(angular velocity)

So, its linear velocity is

b)

The centripetal acceleration of an object in circular motion is given by the equation

where

v is the linear velocity

r is the distance between the object and the axis of rotation

The centripetal acceleration represents the radial acceleration of the object.

For the ladybug in this problem, we have:

v = 3.14 m/s (linear velocity)

r = 1 m (distance)

So, the centripetal acceleration is

c)

The centripetal force for an object in circular motion is given by

where

m is the mass of the object

a is the centripetal acceleration of the object

The centripetal force is the radial inward force that keeps the object in circular motion.

For the ladybug in this problem we have

m = 6.0 kg (mass)

(centripetal acceleration)

So, the centripetal force is

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