Two discs are rotating about their axes, normal to the discs and passing through the centres of the discs. Disc $$D1$$ has $$2$$ kg mass and $$0.2$$ m radius and initial angular velocity of $$50$$ rad $$s-1$$ . Disc $$D2$$ has $$4$$ kg mass, $$0.1$$ m radius and initial angular velocity of $$200$$ $$rads-1$$. The two discs are brought in contact face to face, with their axes of rotation coincident. The final angular velocity (in$$ rad $$s-1$$ $$) of the system is

Question

Two discs are rotating about their axes, normal to the discs and passing through the centres of the discs. Disc $$D1$$ has $$2$$ kg mass and $$0.2$$ m radius and initial angular velocity of $$50$$ rad $$s-1$$ . Disc $$D2$$ has $$4$$ kg mass, $$0.1$$ m radius and initial angular velocity of $$200$$ $$rads-1$$. The two discs are brought in contact face to face, with their axes of rotation coincident. The final angular velocity (in$$ rad $$s-1$$ $$) of the system is

Infinity Learn · Accepted Answer

Moment of inertia of disc $$D1$$ about an axis passing through its centre and normal to its plane $$isI1=MR22=(2$$ $$kg)(0.2$$ $$m)22=0.04$$ kg $$m2$$ Initial angular velocity of disc $$D1$$,ω$$1=50rads-1$$  Moment of inertia of disc $$D2$$ about an axis passing through  it centre and normal to its plane is  $$I2=(4$$ $$kg)(0.1$$ $$m)22=0.02$$ kg $$m2$$  Initial angular velocity of $$discD2$$ω$$2=200rads-1$$  Total initial angular momentum of the two discs is $$Li=I1$$ω$$1+I2$$ω$$2$$ When two discs are brought in contact face to face (one$$ on the top of the $$other) and their axes of rotation coincident the moment of inertia of inertia I of the system is equal to the sum of their individual moment of inertia.$$I=I1+I2Let$$ ω be the final angular speed of the system. The final angular momentum of the system $$isLf=I$$ω$$=I1+I2$$ωAccording to law of conservation of angular momentum, we $$getLi=Lf$$ $$I1$$ω$$1+I2$$ω$$2=I1+I2$$ω ω$$=I1$$ω$$1+I2$$ω$$2I1+I2$$ $$=0.04$$ kg $$m250rads-1+0.02$$ kg $$m2200rads-1(0.04+0.02)kgm2$$ $$=(2+4)0.06rads-1=100rads-1$$

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