a) 3.14 m/s
b) [tex]9.9 m/s^2[/tex]
c) 59.4 N
Explanation:
a)
The relationship between angular velocity and linear velocity for an object in circular motion is given by:
[tex]v=\omega r[/tex]
where
[tex]\omega[/tex] 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)
[tex]\omega=3.14 rad/s[/tex] (angular velocity)
So, its linear velocity is
[tex]v=(3.14)(1)=3.14 m/s[/tex]
b)
The centripetal acceleration of an object in circular motion is given by the equation
[tex]a=\frac{v^2}{r}[/tex]
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
[tex]a=\frac{3.14^2}{1}=9.9 m/s^2[/tex]
c)
The centripetal force for an object in circular motion is given by
[tex]F=ma[/tex]
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)
[tex]a=9.9 m/s^2[/tex] (centripetal acceleration)
So, the centripetal force is
[tex]F=(6.0)(9.9)=59.4 N[/tex]
