What is the average for the following set of measurements 3.1 mL, 2.7 mL, 4.6 mL, 1.9mL, 8.7 mL
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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
angular speed of Susan is
The value is negative because it is in the opposite direction of cockroach.
b) the mechanical energy is not conserved because cockroach stopped in between.