Two wheels A and B are mounted on the same axle. Moment of inertia of A is 6 kg m2 and it is rotating at 600 rpm when B is at rest. What is the moment of inertia of B , if their combined speed is 400 rpm ?

Question

Two wheels A and B are mounted on the same axle. Moment of inertia of A is 6 kg m2 and it is rotating at 600 rpm when B is at rest. What is the moment of inertia of B , if their combined speed is 400 rpm ? (A) 8 kg m2 (B) 4 kg m2 (C) 3 kg m2 (D) 5 kg m2

Tardigrade Admin · Accepted Answer

Applying the principle of conservation of angular momentum, (I1 + I2)ω =I1(ω )1+I2(ω )2 (6 + I2)(400/60)× 2π =6× (600/60)× 2π +I2× 0 Which gives, I2=3 kg m2

Q. Two wheels $A$ and $B$ are mounted on the same axle. Moment of inertia of $A$ is $6 k g m^{2}$ and it is rotating at $600 r p m$ when $B$ is at rest. What is the moment of inertia of $B$ , if their combined speed is $400 r p m$ ?

$8 k g m^{2}$

$4 k g m^{2}$

$3 k g m^{2}$

$5 k g m^{2}$

Applying the principle of conservation of angular momentum,
$(I_{1} + I_{2}) ω = I_{1} (ω)_{1} + I_{2} (ω)_{2}$
$(6 + I_{2}) \frac{400}{60} \times 2 π = 6 \times \frac{600}{60} \times 2 π + I_{2} \times 0$
Which gives, $I_{2} = 3 k g m^{2}$

Q. Two wheels A and B are mounted on the same axle. Moment of inertia of A is 6kgm2 and it is rotating at 600rpm when B is at rest. What is the moment of inertia of B , if their combined speed is 400rpm ?

8kgm2

4kgm2

3kgm2

5kgm2