Question

a phonograph turn table rotates at 78 rpm it's angular speed in rads​

Answer 1

Answer:

Given:

Phonograph Turn Table is rotating at an angular velocity of 78 rpm.

To find:

Angular velocity in rad/s

Concept:

Angular velocity is the rotational analogue of Linear velocity. It's an axial vector directed perpendicular to the plane of circular trajectory of the object.

Relationship with linear velocity is :

$\boxed{ \red{ \large{v = r \: \omega}}}$

Calculation:

For this kind of conversion , follow this rule ;

The phonograph turn Table is rotating 2π angle thereby converting to radians . And for conversion from minute to seconds, divide by 60.

$\huge{ \green{78 \: rpm}}$

$\huge{ \green{ = 78 \times \dfrac{2\pi}{60} \: }}$

$\huge{ \green{ = 2.6 \times \pi \: rad \: {s}^{ - 1} \: }}$

$\huge{ \green{ = 8.168 \: rad \: {s}^{ - 1} \: }}$

So final answer :

$\boxed{ \huge{ \red{ \sf{ \omega = 8.168 \: rad \: {s}^{ - 1} \: }}}}$

Answer 2

$\huge\fcolorbox{red}{pink}{Answer \: :}$

➡ Given:

✏ Frequency of rotation = 78 rpm.

➡ To Find:

✏ Angular velocity in rad/s.

➡ Formula:

✏ Relation between Angular velocity and Frequency of rotation is given by

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \dag \: \underline{ \boxed{ \bold{ \rm{ \pink{ \omega = 2\pi{f}}}}}} \: \dag$

➡ Terms:

✏ $\omega$ denotes angular velocity of phonograph turn table

✏ f denotes frequency of rotation.

➡ Coversation:

✏ Frequency = 78 rpm = 78/60 rps

✏ $\because$ 1 min = 60 sec

➡ Calculation:

$\implies \rm \: \omega = 2\pi \times f \\ \\ \therefore \rm \: \omega = 2\pi \times \frac{78}{60} \\ \\ \therefore \rm \: \omega = 2\pi \times 1.3 \\ \\ \therefore \: \underline{ \boxed{ \bold{ \rm{ \orange{ \omega = 8.164 \: \frac{rad}{s} }}}}} \: \purple{ \clubsuit}$