A diver is diving from a height of 20 m. First, he makes a rotation (body tucked). At the end of this rotation, he is still at 12 m from the water, in vertical position (head up) with an angular velocity of 2??/3 rad/s and a vertical velocity equal to 1.8 m/s downwards. a) How long will it take for him to reach the water? b) To complete another 2.5 rotations, what constant angular velocity must he have from this point on? c) What change must he make to his moment of inertia to achieve this? (express If related to Ii)? Hints: (a) There’s only one equation that uses initial velocity, acceleration and distance into account when determining flight time (remember you don’t know what velocity they’re hitting the water). t ≈ 1.5 s (c) We don’t actually know his moment of inertia, but we can state what proportion it has to change in order to change the angular velocity. Since angular momentum is conserved, Ib.ωb = Ia.ωa. We want an expression for Ib which will include Ia.
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.
A diver is diving from a height of 20 m. First, he makes a rotation (body tucked). At the end of this rotation, he is still at 12 m from the water, in vertical position (head up) with an
a) How long will it take for him to reach the water?
b) To complete another 2.5 rotations, what constant angular velocity must he have from this point on?
c) What change must he make to his moment of inertia to achieve this? (express If related to Ii)?
Hints: (a) There’s only one equation that uses initial velocity, acceleration and distance into account when determining flight time (remember you don’t know what velocity they’re hitting the water). t ≈ 1.5 s
(c) We don’t actually know his moment of inertia, but we can state what proportion it has to change in order to change the angular velocity. Since
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