Question

A device consisting of four heavy balls connected by low-mass rods is free to rotate about an axle. It is initially not spinning. A small bullet traveling very fast buries itself in one of the balls. In the diagram, m = 0.005 kg, v = 450 m/s, M1 = 1.2 kg, M2 = 0.5 kg, R1 = 0.8 m, and R2 = 0.3 m. The axle of the device is at the origin < 0, 0, 0 >, and the bullet strikes at location <0.274, 0.752, 0> m. Just after the impact, what is the angular speed of the device? Note that this is an inelastic collision; the systems temperature increases. angular speed (absolute value of the angular velocity) = _________ radians/s

Answer 1

The angular speed of the device is 1.03 rad/s.

What is the conservation of angular momentum?

A spinning system's ability to conserve angular momentum ensures that its spin will not change until it is subjected to an external torque; to put it another way, the rotation's speed will not change as long as the net torque is zero.

Using the conservation of angular momentum

$L_{i}=L_{f}$

Here,  = the system's angular momentum before the collision

$L_{i}$ = 0 + mv

= (0.005)(450)(0.752)

= 1.692 kgm²/s

The moment of inertia of the system is given by

I = 2(M₁R₁² + M₂R₂²)+ mR₁²

= 2[(1.2)(0.8)² +(0.5)(0.3)²]+0.005(0.8)²

= 1.6292 kgm²

Here,  = Iω

So,

1.692 = 1.6292(ω)

ω = 1.03 rad/s

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Answer 2

The angular speed of the device is 1.03 rad/s.

What is the conservation of angular momentum?

A spinning system's ability to conserve angular momentum ensures that its spin will not change until it is subjected to an external torque; to put it another way, the rotation's speed will not change as long as the net torque is zero.

Using the conservation of angular momentum
$L_{i} = L{f}$

Here, $L_{i}$ = the system's angular momentum before the collision

$L_{i}$ = 0 + mv$d_{y}$

= (0.005)(450)(0.752)

= 1.692 kgm²/s

The moment of inertia of the system is given by

I = 2(M₁R₁² + M₂R₂²)+ mR₁²

= 2[(1.2)(0.8)² +(0.5)(0.3)²]+0.005(0.8)²

= 1.6292 kgm²

Here, $L_{f}$ = Iω

So,

1.692 = 1.6292(ω)

ω = 1.03 rad/s

To know more about the conservation of angular momentum, visit:

brainly.com/question/1597483

#SPJ1