Answer:
v = 3.77 m/s
Step-by-step explanation:
Uniform Circular Motion
It's a movement in which an object moves along the circumference of a circle. It can also be defined as a rotation along a circular path.
The angular speed can be calculated in two different ways:
[tex]\displaystyle \omega=\frac{v}{r}[/tex]
Where:
v = tangential or linear speed
r = radius of the circle described by the rotating object
Also:
[tex]\omega=2\pi f[/tex]
Where:
f = frequency
The frequency is calculated when the number of revolutions n and the time t are known:
[tex]\displaystyle f=\frac{n}{t}[/tex]
The pulley turns at n=6 revolutions per t= 1 second, thus:
[tex]\displaystyle f=\frac{6}{1}[/tex]
f = 6 Hz
The angular speed is:
[tex]\omega=2\pi 6[/tex]
[tex]\omega=37.7 \ rad/s[/tex]
The linear speed can be calculated by solving the first equation for v:
[tex]v = \omega\cdot r[/tex]
The radius is converted to meters: r=10 cm = 0.1 m. Calculate the speed:
[tex]v = 37.7 \ rad/s\cdot 0.1\ m[/tex]
v = 3.77 m/s
