Question

Two solid discs are liked with a belt. The

diameterof the larger disc is twice as large as the diameter of the
smalldisc. If the small disc is rotating at 500 revolutions per
minute(rpm), what is the rotational speed of the large disc?
Express youranswer in rpm and in radians.

Answer 1

ω₂ = 13.09 rad/s

Step-by-step 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 = (1)/(2)MR^2`

now,

`((1)/(2)MR_1^2)\omega_1=((1)/(2)MR_2^2)\omega_2`

`((1)/(2)MR^2)\omega_1=((1)/(2)M(2R)^2)\omega_2`

`R^2* \omega_1= 4 R^2* \omega_2`

`\omega_2=(\omega_1)/(4)`

`\omega_2=(500)/(4)`

ω₂ = 125 rpm

and

`\omega_2=125* (2\pi)/(60)`

ω₂ = 13.09 rad/s

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