Abelt 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.

Part a)

Part b)

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

To convert rev to rad, multiply by 2π

Part b) Find the linear speed in inches per minute

we know that

The circumference of a circle is equal to

we have

----> given problem

substitute

Remember that

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

so

To convert rev to in, multiply by 16π

- "runner b is moving at a slower rate."

- "the graphs shown are graphs of distance(km) against time(min).

the slopes of this graphs are are given by:

slope = (change in y)/(change in x)

= (change in distance)/(change in time)

this is the formula for finding the speed. so, the slope of these graphs represent the speed of the runner.

taking each division in the graph to represent 1 on both axis:

runner a ⇒ speed = (2-0)/(1-0)

= 2/1

= 2 km/min

runner b ⇒ speed = (3-0)/(3-0)

= 3/3

= 1 km/min

this shows that   runner b is moving at a slower rate."