Question

A diver having moment of inertia 6 kgm about an axis through center of mass rotates at
2rad/s. if he folds his hands and feet to decrease the moment of inertia to 5kgm?, the new
angular velocity is
A 2 rad/s
C) 2.2 rad/s
8 24 rad/s
D) 1.67 rad/s​

Answer 1

Answer:

2.4 rad/s

is the correct answer

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Answer 2

Given:-

• A diver having moment of inertia 6 kgm about an axis through center of mass rotates at 2rad/s.
• he folds his hands and feet to decrease the moment of inertia to 5kgm

i.e

$I _ 1 = 6 kg {m}^{2}$

$ω _ 1 = 2 rad/s$

$I_ 2 = 5 kg{m}^{2}$

To Find:-

• the new angular velocity.

Solution:-

External Torque=0

From Conservation of Angular momentum

$\sf \: I_1=I_2$

$= > I_2 \times ω_1 =I_2 \times ω_2$

$= > 2 \times 6 = 5 \times ω_2$

$= > ω_2 = \frac{12}{5}$

$= > ω_2 = 2.4rad {s}^{ - 1}$

∴ the new angular velocity is 2.4rad/s