Rotational Motion and Artificial Gravity Quiz

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Questions and Answers

What is the relationship between torque, moment of inertia, and angular acceleration as defined in the content?

  • Torque equals the moment of inertia divided by angular acceleration.
  • Torque equals the square of the radius times angular acceleration.
  • Torque equals the moment of inertia times angular acceleration. (correct)
  • Torque equals the force times the distance from the axis of rotation.

How can weightlessness be experienced inside the International Space Station?

  • Through constant free fall. (correct)
  • By using anti-gravity technology.
  • By moving at high speeds in a straight line.
  • By being millions of miles from Earth's gravitational influence.

What does the term 'moment of inertia' refer to in the context of rotational motion?

  • The force required to rotate an object at a constant speed.
  • The quantity that determines an object's resistance to angular acceleration. (correct)
  • The total mass of an object in motion.
  • The distance from the center of mass to the point of rotation.

Which of the following correctly describes the force acting on a mass rotating at a distance 'r' from the axis of rotation?

<p>It must be tangential to the path of the mass. (A)</p> Signup and view all the answers

Which equation represents the definition of torque when considering a mass rotating at a distance 'r'?

<p>Ï„ = r * F (A)</p> Signup and view all the answers

What is the primary purpose of artificial gravity in space stations?

<p>To counteract the effects of weightlessness (B)</p> Signup and view all the answers

Which equation represents the relationship between linear velocity, centripetal acceleration, and radius in creating artificial gravity?

<p>$v = ext{sqrt}(a imes R)$ (D)</p> Signup and view all the answers

What negative effects can prolonged weightlessness cause that artificial gravity aims to alleviate?

<p>Weakened bones and muscles (A)</p> Signup and view all the answers

In a rotating space station, what does the centripetal acceleration at the outer rim equal?

<p>The acceleration due to gravity (A)</p> Signup and view all the answers

What is the angular velocity of a satellite if the radius is 1500 m and the artificial gravity is 9.8 m/s²?

<p>0.08 rad/s (B)</p> Signup and view all the answers

Which of the following is NOT a difficulty faced by astronauts in a rotating space station?

<p>Enhanced mobility (B)</p> Signup and view all the answers

What is the time period for one rotation for a satellite with a radius of 1500 m under artificial gravity of 9.8 m/s²?

<p>77.8 s (C)</p> Signup and view all the answers

If the frequency of a satellite is 0.01286 Hz, what is the corresponding time period?

<p>77.8 s (D)</p> Signup and view all the answers

Which formula correctly relates the linear and angular velocity of a satellite?

<p>v = ωR (B)</p> Signup and view all the answers

What will happen to the frequency of a satellite if the radius increases while the artificial gravity remains constant?

<p>Decrease (B)</p> Signup and view all the answers

Flashcards

Torque

The twisting force that causes rotational acceleration.

Moment of Inertia

A measure of an object's resistance to changes in its rotational motion.

Angular Acceleration

The rate at which an object's angular velocity changes over time.

Torque Equation (4.23)

Torque equals moment of inertia times angular acceleration.

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Weight in Space

Force of gravity is not zero, but the astronauts float because they are still in free-fall.

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Weightlessness

The sensation of being without weight

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Free-Fall

Motion of an object where the only force acting on it is gravity.

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Space Stations

Orbit Earth at a speed that keeps them in constant state of free fall, creating an environment of weightlessness for astronauts

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International Space Station (ISS)

A large space station orbiting Earth.

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Artificial Gravity

A technique in space stations that creates the sensation of gravity using rotation.

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Centripetal Acceleration

The acceleration of an object moving in a circular path, always directed towards the center of the circle.

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Linear Velocity (v)

The speed of an object moving in a straight line.

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Radius (R)

The distance from the center of the rotating station to any point on the outer rim.

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Artificial Gravity Equation

v = √(a × R), where v is velocity, a is centripetal acceleration, and R is radius. This equation calculates the velocity needed for a specific level of artificial gravity.

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Weightlessness in space

The lack of apparent weight experienced due to the absence of sufficient support forces.

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Effects of weightlessness

Prolonged weightlessness can lead to bone and muscle weakening.

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Angular Velocity (ω)

The rate at which an object rotates or revolves around an axis.

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Linear Velocity (v)

The speed at which an object moves in a straight line.

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Relationship v = ωR

Linear velocity (v) equals angular velocity (ω) multiplied by the radius (R).

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Satellite's Angular Velocity (ω)

The angular speed needed for a satellite to orbit with artificial gravity.

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Satellite's Time Period (T)

The time a satellite takes to complete one full orbit.

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Satellite's Frequency (f)

The number of orbits a satellite completes per unit time.

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Artificial Gravity

Centripetal force that mimics the Earth's gravity.

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