Question

72. A circular disc is rotating about its natural axis
with angular velocity of 10 rads-1 A second
disc of same mass is joined to it coaxially. If
the radius of disc is half of the radius of the
first, then they together rotate with an angular
velocity of

1) 2.5 rads-1
2) 5 rads-1
3) 8 rads-1
4) 6 rads-1​

Answer 1

Answer:

option (3) is correct

Explanation:

In this case angular momentum will be conserved.

Finally both the discs will rotate with same angular speed.

Linitial = Lfinal

L=Iw

(MR^2)10/2 = (MR^2)w/2 + (MR^2)w/8

w=8 rad/sec

Answer 2

When both disc rotate together , then the angular velocity=$8 rad/s$

Explanation:

In first case

Let radius of disc=$r_1=r$

Angular velocity of circular disc=$10 rad/s$

Moment of inertia=$I_1=M\frac{r^2}{2}$

In second case

Let angular velocity=$\omega_2$

Radius of circular disc=$r_2=\frac{r_1}{2}$

When they rotate together , then

Moment of inertia=$I_2=\frac{Mr^2}{2}+\frac{Mr^2}{8}$

Angular momentum=L=$I\omega$

Where I=Moment of inertia

$\omega$=Angular velocity

Since, there is no external torque so angular  momentum is conserved .

$L_1=L_2$

$I_1\omega_1=I_2\omega_2$  

Substitute the values then we get

$\frac{Mr^2}{2}(10)=(\frac{Mr^2}{2}+\frac{Mr^2}{8})\omega_2$

$5Mr^2=\frac{5}{8}Mr^2\omega_2$

$\omega_2=\frac{5Mr^2\times 8}{5Mr^2}=8$

Hence, when both disc rotate together then, the  angular velocity=$8rad/s$

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