Question

A belt runs a pulley of radius 8 inches at 60 revolutions per minute. a) Find the angular speed in radians per minute. b) Find the linear speed in inches per minute.

Answer 1

Answer:

Part a) $120\pi\ \frac{rad}{min}$

Part b) $960\pi\ \frac{in}{min}$

Step-by-step explanation:

we have

60 rev/min

Part a) Find the angular speed in radians per minute

we know that

One revolution represent 2π radians (complete circle)

so

$1\ rev=2\pi \ rad$

To convert rev to rad, multiply by 2π

$60\ \frac{rev}{min}=60(2\pi)=120\pi\ \frac{rad}{min}$

Part b) Find the linear speed in inches per minute

we know that

The circumference of a circle is equal to

$C=2\pi r$

we have

$r=8\ in$ ----> given problem

substitute

$C=2\pi(8)$

$C=16\pi\ in$

Remember that

One revolution subtends a length equal to the circumference of the circle

so

$1\ rev=16\pi\ in$

To convert rev to in, multiply by 16π

$60\ \frac{rev}{min}=60(16\pi)=960\pi\ \frac{in}{min}$