A disk with moment of inertia I1 rotates about a frictionless, vertical axle with angular speed ωi A second disk, this one having moment of inertia I2 and initially not rotating, drops onto the first disk (Fig.). Because of friction between the surfaces, the two eventually reach the same angular speed ωf The value of ωf is

Question

A disk with moment of inertia I1 rotates about a frictionless, vertical axle with angular speed ωi A second disk, this one having moment of inertia I2 and initially not rotating, drops onto the first disk (Fig.). Because of friction between the surfaces, the two eventually reach the same angular speed ωf The value of ωf is (A) (I1+I2/I1) ωi (B) (I1/I1+I2) ωi (C) (I1+I2/I2) ωi (D) (I1/I2) ωi

Tardigrade Admin · Accepted Answer

From conservation of angular momentum for the isolated system of two disks: (I1+I2) ωf=I1 ωi text or ωf .=(I1/I1+I2) ωi

$\frac{I _{1} + I _{2}}{I _{1}} ω_{i}$

$\frac{I _{1}}{I _{1} + I _{2}} ω_{i}$

$\frac{I _{1} + I _{2}}{I _{2}} ω_{i}$

$\frac{I _{1}}{I _{2}} ω_{i}$

From conservation of angular momentum for the isolated system of two disks:
$(I_{1} + I_{2}) ω_{f} = I_{1} ω_{i} or ω_{f .} = \frac{I _{1}}{I _{1} + I _{2}} ω_{i}$

I1​I1​+I2​​ωi​

I1​+I2​I1​​ωi​

I2​I1​+I2​​ωi​

I2​I1​​ωi​

From conservation of angular momentum for the isolated system of two disks: (I1​+I2​)ωf​=I1​ωi​ or ωf.​=I1​+I2​I1​​ωi​

$\frac{I _{1} + I _{2}}{I _{1}} ω_{i}$

$\frac{I _{1}}{I _{1} + I _{2}} ω_{i}$

$\frac{I _{1} + I _{2}}{I _{2}} ω_{i}$

$\frac{I _{1}}{I _{2}} ω_{i}$

From conservation of angular momentum for the isolated system of two disks:
$(I_{1} + I_{2}) ω_{f} = I_{1} ω_{i} or ω_{f .} = \frac{I _{1}}{I _{1} + I _{2}} ω_{i}$