Centrifuge

Study centripetal acceleration and g-force in circular motion by varying the rotation speed and radius with the FizziQ Web Centrifuge simulation.

Astronauts train in giant centrifuges that subject them to accelerations of 6 to 9 g, simulating the forces of a rocket launch. But how is this acceleration calculated? Does it depend more on the rotation speed or on the arm length? The FizziQ Web Centrifuge simulation lets you explore the relationship between centripetal acceleration, angular velocity, and radius, and understand why doubling the rotation speed quadruples the acceleration.

Visão geral da atividade:

The student uses the FizziQ Web Centrifuge simulation to measure centripetal acceleration by varying the rotation speed (at fixed radius) then the radius (at fixed speed). They verify the relationship a = ω²r and connect the results to g-force thresholds.

Nível:

High school

FizziQ Web

Autor:

Duração (minutos):

30

O que os alunos farão:

- Measure centripetal acceleration for different rotation speeds and radii
- Verify the relationship a = ω²r experimentally
- Understand g-force as the ratio of acceleration to gravitational acceleration
- Plot a versus ω² and a versus r to confirm proportionality
- Calculate the rotation speed needed to simulate different gravity levels

Conceitos científicos:

- Centripetal acceleration
- Angular velocity (ω in rad/s)
- Relationship a = ω²r
- G-force
- Uniform circular motion
- Centripetal force

Sensores:

- FizziQ Web Centrifuge simulation

Materiais necessários:

- Computer, tablet, or smartphone with FizziQ Web

Procedimento experimental:

Open the Centrifuge simulation in FizziQ Web (Experiment → Simulations → Centrifuge).
Part 1 — Effect of speed: set the radius to 5 m. Set the rotation speed to 10 rpm and start the simulation.
Note the centripetal acceleration and g-factor displayed. Stop the recording.
Repeat for speeds 20, 30, 40, 50, and 60 rpm. Create a table: Speed (rpm), ω (rad/s), ω² (rad²/s²), Acceleration (m/s²), g-factor.
To convert: ω (rad/s) = speed (rpm) × 2π / 60. Calculate ω and ω² for each speed.
Plot the graph of acceleration versus ω². Is it a straight line? The slope should equal r = 5 m.
Part 2 — Effect of radius: set the speed to 30 rpm. Vary the radius: 2, 4, 6, 8, 10 m.
Note the centripetal acceleration for each radius. Plot a versus r. The straight line confirms that a is proportional to r.
From your data, determine which speed-radius combination gives a g-factor of 3 (the threshold where untrained people may lose consciousness).
Conclusion: the relationship a = ω²r shows that acceleration depends on the square of speed but only linearly on radius. Doubling the speed quadruples the acceleration.

Resultados esperados:

For r = 5 m: at 10 rpm, ω = 1.05 rad/s, a = 5.5 m/s² (0.56 g). At 30 rpm, ω = 3.14 rad/s, a = 49.3 m/s² (5.0 g). At 60 rpm, ω = 6.28 rad/s, a = 197 m/s² (20.1 g). The graph a(ω²) is a straight line with slope 5 m (equal to the radius). The graph a(r) at 30 rpm is a straight line with slope ω² ≈ 9.87 rad²/s². All results confirm a = ω²r.

Questões científicas:

- Why does the acceleration depend on the square of angular velocity rather than simply on velocity?
- If you double the radius at constant angular velocity, the acceleration doubles. But if you double the tangential speed at constant radius, what happens?
- Why do car passengers feel pushed outward in a turn even though the acceleration is directed inward?
- What radius and rotation speed would be needed to simulate Earth's gravity in a 100 m diameter space station?
- Why are professional centrifuges built with long arms rather than short arms spinning very fast?
- What is the difference between centripetal acceleration and centrifugal force?

Explicações científicas:

In circular motion, an object constantly changes direction even if its speed is constant. This change of direction implies an acceleration directed toward the center of the circle: the centripetal acceleration a = ω²r = v²/r.

The angular velocity ω is expressed in rad/s. To convert from revolutions per minute: ω = N × 2π / 60, where N is the number of rpm.

The g-factor is the ratio of the acceleration experienced to Earth's gravitational acceleration: g-factor = a / 9.81. A g-factor of 1 means the person feels their normal weight. At 3g, they feel three times heavier.

The dependence on ω² has an important consequence: doubling the rotation speed quadruples the acceleration. This is why centrifuges are potentially dangerous: a small speed increase produces a large acceleration increase.

Physiological effects vary with intensity: at 2-3 g, blood pools in the legs. At 4-6 g, an untrained person may lose consciousness. At 9 g, even trained pilots with g-suits are at their limit.

Atividades de extensão:

Perguntas frequentes:

Q: The rotation speed is in rpm but the formulas use ω in rad/s. How do I convert?
R: Multiply the number of revolutions per minute by 2π/60. For example: 30 rpm × 2π/60 = 3.14 rad/s.

Q: Why does the acceleration not depend on the mass of the object?
R: The formula a = ω²r gives the acceleration, which is a kinematic quantity independent of mass. The force needed to maintain circular motion does depend on mass (F = ma), but the acceleration does not.

Q: What is the difference between centripetal and centrifugal force?
R: Centripetal force is the real force directed inward that keeps the object on a circular path. Centrifugal force is an apparent force felt in the rotating reference frame, directed outward. Only centripetal force exists in an inertial frame.

Q: Can the simulation model gravitational effects like blood pooling?
R: No, the simulation only computes the acceleration value. The physiological effects are inferred from the g-factor and known human tolerance thresholds.