Question

Two solid discs are liked with a belt. The

Answer 1

Answer:

ω₂ = 13.09 rad/s

Explanation:

given,

small disk rotating speed = 500 rpm

radius of small disk = R

radius of larger disk = 2 R

rotational speed of larger disk = ?

using the law of conservation of angular momentum, we get

I₁ ω₁ = I₂ ω₂

moment of inertia for solid disk

$I = \dfrac{1}{2}MR^2$

now,

$(\dfrac{1}{2}MR_1^2)\omega_1=(\dfrac{1}{2}MR_2^2)\omega_2$

$(\dfrac{1}{2}MR^2)\omega_1=(\dfrac{1}{2}M(2R)^2)\omega_2$

$R^2\times \omega_1= 4 R^2\times \omega_2$

$\omega_2=\dfrac{\omega_1}{4}$

$\omega_2=\dfrac{500}{4}$

   ω₂ = 125 rpm

and

$\omega_2=125\times \dfrac{2\pi}{60}$

   ω₂ = 13.09 rad/s

the rotational speed of larger disc is equal to ω₂ = 13.09 rad/s