Physics: Four particles, each of mass 0.16 kg are placed at the vertices of a square with sides of length 0.42 m the particles are connected by rods of negligible mass. this rigid body can rotate in a vertical plane about a horizontal axis a that passes through one of the particles. the body is released from rest with rod ab horizontal, as shown in the figure.(a) what is the rotational inertia of the body about axis a? (b) what is the angular speed of the body about axis a at the instant rod ab swings through

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Four particles, each of mass 0.16 kg are placed

Ответ:

gabe7774

16.01.2022

Physics

0.112896 kgm²

6.83478497937 rad/s

Explanation:

m = Mass of each particle = 0.16 kg

l = Length of side = 0.42 m

$\omega$ = Angular speed

g = Acceleration due to gravity = 9.81 m/s²

Moment of inertia would be given by

$I=0+ml^2+m(\sqrt2 l)^2+ml^2\\\Rightarrow I=ml^2+m2l^2+ml^2\\\Rightarrow I=4ml^2\\\Rightarrow I=4\times 0.16\times 0.42^2\\\Rightarrow I=0.112896\ kgm^2$

Rotational inertia of the body about axis A is 0.112896 kgm²

Applying conservation of energy

$4mgl=\dfrac{1}{2}I\omega^2\\\Rightarrow \omega=\sqrt{\dfrac{4mgl\times 2}{I}}\\\Rightarrow \omega=\sqrt{\dfrac{4\times 0.16\times 9.81\times 0.42\times 2}{0.112896}}\\\Rightarrow \omega=6.83478497937\ rad/s$

The angular speed is 6.83478497937 rad/s

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