Respuesta :
Answer
given,
mass of cockroach = 0.117 Kg
radius = 17.3 cm
rotational inertia = 5.20 x 10⁻³ Kg.m²
speed of cockroach = 1.91 m/s
angular velocity of Susan (ω₀)= 2.87 rad/s
final speed of cockroach = 0 m/s
Initial angular velocity of Susan
L_s = I ω₀
L_s = 5.20 x 10⁻³ x 2.87
L_s=0.015 kg.m²/s
initial angular momentum of the cockroach
L_c = - mvr
L_c = - 0.117 x 1.91 x 0.173
L_c = - 0.0387 kg.m²/s
total angular momentum of Both
L = 0.015 - 0.0387
L = - 0.0237 kg.m²/s
after cockroach stop inertia becomes
I_f = I + mr^2
I_f = 5.20 x 10⁻³+ 0.117 x 0.173^2
I_f = 8.7 x 10⁻³ kg.m²/s
final angular momentum of the disk
L_f = I_f ω_f
L_f = 8.7 x 10⁻³ x ω_f
using conservation of momentum
L_i = L_f
-0.0237 =8.7 x 10⁻³ x ω_f
[tex]\omega_f = \dfrac{-0.0237}{8.7 \times 10^{-3}}[/tex]
[tex]\omega_f = -2.72\ rad/s[/tex]
angular speed of Susan is [tex]\omega_f = -2.72\ rad/s[/tex]
The value is negative because it is in the opposite direction of cockroach.
[tex]|\omega_f |= 2.72\ rad/s[/tex]
b) the mechanical energy is not conserved because cockroach stopped in between.
