A disc of moment of inertia I, is rotating freely with angular velocity ω1 when a second, non rotating disc with moment of inertia I2 is dropped on it gently the two then rotate as a unit. Then the total angular speed is.

Question

A disc of moment of inertia I, is rotating freely with angular velocity ω1 when a second, non rotating disc with moment of inertia I2 is dropped on it gently the two then rotate as a unit. Then the total angular speed is. (A) (I1 ω1/I2) (B) (I2 ω1/I2+I2) (C) (I1 ω1/I1+I2) (D) ((I1+I2)/I2) ω1

Tardigrade Admin · Accepted Answer

According to the conservation of angular momenturm I ω= constant When second disc is dropped on it and forms a unit I1 ω1=(I1+I2) ω2 (angular momentum always constant) (I1 ω1/I1+I2)=ω2

Q. A disc of moment of inertia $I$ , is rotating freely with angular velocity $ω_{1}$ when a second, non rotating disc with moment of inertia $I_{2}$ is dropped on it gently the two then rotate as a unit. Then the total angular speed is.

$\frac{I _{1} ω _{1}}{I _{2}}$

$\frac{I _{2} ω _{1}}{I _{2} + I _{2}}$

$\frac{I _{1} ω _{1}}{I _{1} + I _{2}}$

$\frac{( I _{1} + I _{2} )}{I _{2}} ω_{1}$

According to the conservation of angular momenturm
$I ω =$ constant
When second disc is dropped on it and forms a unit
$I_{1} ω_{1} = (I_{1} + I_{2}) ω_{2}$
(angular momentum always constant)
$\frac{I _{1} ω _{1}}{I _{1} + I _{2}} = ω_{2}$

Q. A disc of moment of inertia I, is rotating freely with angular velocity ω1​ when a second, non rotating disc with moment of inertia I2​ is dropped on it gently the two then rotate as a unit. Then the total angular speed is.

I2​I1​ω1​​

I2​+I2​I2​ω1​​

I1​+I2​I1​ω1​​

I2​(I1​+I2​)​ω1​