Question

Calculate the angular speed of the wheel making
240 revolutions per minute
a) 40r rads-1
b) rads-1
c)60 i rads-1
d)8 i rads-​

Answer 1

Explanation:

The formula for calculating angular speed of any rotating body =2*pi*N/60

where N is RPM of rotating body

if N=240

then angular speed of flyweel=2*pi*240/60=25.13

hence angular speed of flyweel making 240 revolutions per minute is 25.13 radian per second

Answer 2

Given :

Frequency $(\nu)$= 240 rpm

To find :

Angular velocity $(\omega)$

Solution :

Converting rpm (revolution per minute) to rps (revolution per second)

240 rpm into rps

= 240/60

= 4 rps

Therefore the revolution made per second are 4 .

By the formula of angular velocity :

$\boxed{\tt \large \omega = 2 \pi \nu}$

$\tt \implies \omega = 2 \times 3.14 \times 4$

$\implies \tt \omega = 25.12 \: rad {s}^{ - 1}$

_________________________

Angular velocity is the angle ∅ wiped by radius vector r in a given time t .

It is given by :

$\boxed{\begin{minipage}{3 cm} \star \: \tt \omega = \dfrac{d\theta}{dt} \\ \\ \star \: \omega = \dfrac{2 \pi}{t} \\ \\ \star \: \omega = 2 \pi \nu \end{minipage}}$

Where , ∅ = angular displacement , t = time period , $\nu$ = frequency .

Its SI unit is rad/s .