Answer to Question #249678 in Classical Mechanics for aisme

Question

A 1.6 kg cat X at 1.2 m apart from the axis of rotation through point O on the platform that rotates horizontally (anti-clockwise) without friction. The platform has moment of inertia 80.0 kgm^2 and radius 2.0 m. The platform initially at rest, starts to rotate under a tangential force F of constant magnitude 25.0 N. Calculate the

(a) moment of inertia for the whole rotating system.

(b) angular acceleration of the system.

(c) angular speed of the system after 9.0 s.

(d) angular momentum of the system after 9.0 s.

Answer 1

a)

$I_2=ml^2,$

$I=I_1+I_2=80+1.6\cdot 1.2^2=82.3~kg\cdot m^2,$

b)

$\epsilon=\frac MI=\frac{Fr}I=0.61~\frac{rad}{s^2},$

c)

$\omega=\epsilon t=5.5~\frac {rad}s,$

d)

$L=I\omega=450~\frac{kg\cdot m^2}s.$