Question

A pulley of radius 10cm turns at 6 revolutions per second. What is the linear velocity of the belt driving the pulley in meters per second?
1.67 m/s
3.77 m/s
376.99 m/s
166.67 m/s

Answer 1

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:

$\displaystyle \omega=\frac{v}{r}$

Where:

v = tangential or linear speed

r = radius of the circle described by the rotating object

Also:

$\omega=2\pi f$

Where:

f = frequency

The frequency is calculated when the number of revolutions n and the time t are known:

$\displaystyle f=\frac{n}{t}$

The pulley turns at n=6 revolutions per t= 1 second, thus:

$\displaystyle f=\frac{6}{1}$

f = 6 Hz

The angular speed is:

$\omega=2\pi 6$

$\omega=37.7 \ rad/s$

The linear speed can be calculated by solving the first equation for v:

$v = \omega\cdot r$

The radius is converted to meters: r=10 cm = 0.1 m. Calculate the speed:

$v = 37.7 \ rad/s\cdot 0.1\ m$

v = 3.77 m/s