Question

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.

Answer 1

a) 3.14 m/s

b) $9.9 m/s^2$

c) 59.4 N

Explanation:

a)

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

$v=\omega r$

where

$\omega$ 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)

$\omega=3.14 rad/s$ (angular velocity)

So, its linear velocity is

$v=(3.14)(1)=3.14 m/s$

b)

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

$a=\frac{v^2}{r}$

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

$a=\frac{3.14^2}{1}=9.9 m/s^2$

c)

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

$F=ma$

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)

$a=9.9 m/s^2$ (centripetal acceleration)

So, the centripetal force is

$F=(6.0)(9.9)=59.4 N$