Respuesta :
Answer:
Explanation:
- let m1 = 2 kg
- r1 = 60 cm = 0.6 m
- w1 = -20 rev/s (clockwise)
I1 = 0.5 x m1 x r1²
= 0.5 x 2 x 0.6²
= 0.36 kg.m²
m2 = 2 kg
r2 = 40 cm = 0.4 m
w2 = 20 rev/s (counter clockwise)
I2 = 0.5 x m2 x r2²
= 0.5 x 2 x 0.4²
= 0.16 kg.m²
let wf be the final angular velocity of the two disks.
Applying conservation of angular momentum ;
(I1 + I2) x wf = I1 x w1 + I2 x w2
wf = (I1 x w1 + I2 x w2) / (I1 + I2)
= (0.36 x (-20) + 0.16 x 20 )/(0.36 + 0.16)
= -7.69rev/s
The negative sign indicates the disks rotate clockwise direction.
The required value is,
[tex]|w_f| = 15.4\ rev/s[/tex]
Conservation of angular momentum:
The angular momentum of a system of particles around a point in a fixed inertial reference frame is conserved if there is no net external torque around that point is conserved. Any of the individual angular momenta can change as long as their sum remains constant.
Let us assume that,
[tex]m_1 = 2 kg\\r_1 = 60 cm = 0.6 m\\w_1 = -40 rev/s (clockwise)[/tex]
[tex]I_2 = 0.5\times m_2\times (r_2)^2\\= 0.5\times 2\times0.4^2\\= 0.16 kgm^2[/tex]
Let [tex]w_f[/tex] is the final angular velocity of the two disks.
Apply conservation of angular momentum,
[tex](I_1 + I_2)w_f = I_1\times w_1 + I_2\times w_2\\w_f = \frac{(I_1\times w_1 + I_2\times w_2)}{(I_1 + I_2)} \\= \frac{(0.36\times (-20) + 0.16\times 20 )}{(0.36 + 0.16)} \\w_f= -7.69 \ rev/s\\|w_f|=15.4 \ ref/s[/tex]
The negative sign indicates the disks rotate clockwise direction.
Learn more about the topic Conservation of angular momentum:
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