two identical spherical shells connected with a tube. The radius and the mass of a shell are r = 5.0 m and ?=2500 kg, respectively. The whole station is rotating about the centre at a constant angular speed, ? = 7.2 ??? to generate artificial gravity. The length of the tube is 12 m and the mass is negligible compared to the shells. (a) Calculate the rotational inertia of the space station.(Given that the rotational inertia of a spherical shell about the axis through its centre is ???cm =2/3? ? ^2) (b) Calculate the rotational kinetic energy of the space station. (c) Calculate the angular momentum of the space station.
Simple harmonic motion
Simple harmonic motion is a type of periodic motion in which an object undergoes oscillatory motion. The restoring force exerted by the object exhibiting SHM is proportional to the displacement from the equilibrium position. The force is directed towards the mean position. We see many examples of SHM around us, common ones are the motion of a pendulum, spring and vibration of strings in musical instruments, and so on.
Simple Pendulum
A simple pendulum comprises a heavy mass (called bob) attached to one end of the weightless and flexible string.
Oscillation
In Physics, oscillation means a repetitive motion that happens in a variation with respect to time. There is usually a central value, where the object would be at rest. Additionally, there are two or more positions between which the repetitive motion takes place. In mathematics, oscillations can also be described as vibrations. The most common examples of oscillation that is seen in daily lives include the alternating current (AC) or the motion of a moving pendulum.
two identical spherical shells connected with a tube. The radius and the mass of a shell are r = 5.0 m and ?=2500 kg, respectively. The whole station is rotating about the centre at a constant angular speed, ? = 7.2 ??? to generate artificial gravity. The length of the tube is 12 m and the mass is negligible compared to the shells.
(a) Calculate the rotational inertia of the space station.(Given that the rotational inertia of a spherical shell about the axis through its centre is ???cm =2/3? ? ^2)
(b) Calculate the rotational kinetic energy of the space station.
(c) Calculate the
(d) Unfortunately, a 200 kg space probe hit one of the shells tangentially with a speed 12 ms-1 and embedded into the centre of the shell. The size of the probe is negligible compared to the size of the station. This means the probe can be treated as a point mass. Calculate the angular speed of the of the station after it was hit.
(e) Check if the total kinetic energy of the space station – probe system conserved after the impact.
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