Question

A wheel completes 5.6 revolutions in 8 seconds.

Answer 1

Answer:

$86.15\pi rad/min$

Explanation: Angular velocity is the number of revolutions made per unit time.

We convert the number of revolutions to radians and the time given in seconds to minutes,

Given;

$1rev=2\pi rad\\therefore\\5.6rev=5.6*2\pi rad\\= 11.2\pi rad$

Also,

60s = 1 min

hence

$8s=\frac{8}{60}min\\=0.13min$

We now divide the number of revolution in radians by the time in minutes.

$\omega =\frac{11.2\pi}{0.13min}\\\omega=86.15\pi rad/min$

Answer 2

Answer:

the angular velocity in rad per minute would be  263.89 rad/min

Explanation:

Angular Velocity is the velocity of a body along a circular path, it is measured in rev/min,  rad/m.

Given that the wheel has

rev = 5.6

time = 8 sec = 8 /60 =  2/15 minute

The angular velocity  in rev/min would be;

ω = no. of revolution/time

ω = 5.6 rev /  (2/15 minute)

ω = 5.6 rev x 15/2 minute

 ω   = 42 rev/minute

the angular velocity in rev/minute is 42 rev/minute and to convert the angular velocity to rad/minute we have;

1 rev = 2π rad/min

42 rev/min = 42 rev/min x 2π rad/min

                   = 263.89 rad/min

Therefore the angular velocity in rad per minute would be

263.89 rads/min