How far along circular arch is an astronaut

  • Thread starter Thread starter sweetwilliam
  • Start date Start date
  • Tags Tags
    Astronaut Circular
Click For Summary
SUMMARY

The discussion revolves around calculating the distance an astronaut in chamber B travels along a circular arc when an astronaut in chamber A moves 240 meters. Given the radii of the chambers, r(A) = 320 meters and r(B) = 1100 meters, the relationship between the distances can be established using the formula for arc length, s = θ × r. The correct approach involves using the proportion of the radii to determine the arc length for chamber B, confirming that both chambers share the same angle θ during the rotation.

PREREQUISITES
  • Understanding of circular motion and arc length
  • Familiarity with the formula for arc length: s = θ × r
  • Basic knowledge of proportions in geometry
  • Concept of angular displacement in rotational motion
NEXT STEPS
  • Study the derivation and applications of the arc length formula in circular motion
  • Explore the relationship between linear and angular velocity in rotational dynamics
  • Learn about the principles of rotational kinematics and dynamics
  • Investigate the effects of radius on the motion of objects in circular paths
USEFUL FOR

Students studying physics, particularly those focusing on circular motion and dynamics, as well as educators seeking to clarify concepts related to arc length and proportional reasoning in rotational systems.

sweetwilliam
Messages
12
Reaction score
0

Homework Statement


a space station consists of two donut shaped living chambers A and B, that have radii r(A)= 3.2x10^2m and r(B)=1.10x10^3m. As the station rotates, the astronaut in chamber A is moved 2.40x10^2 m along a circular arc. how far along a circular arc is an astronaut in chamber B moved during the same time?


Homework Equations





The Attempt at a Solution


i used a proportion r(A)/ circular arc = r(B)/ x and solved for x i got the correct answer but my
but i was wondering if there was a different way to solve this using formulas...my physics prof. would not be happy if i didnt use correct formulas. thanks!
 
Physics news on Phys.org
Do you remember the formula for arc length? Find θ, it will be the same for both living chambers. Do you see why your approach also works using the arc length formula?
 
s=theta x r i see now how that works...thanks so much, i didnt think of that at first. thanks
 

Similar threads

Problem 9.2 Classical Mechanics: Astronaut in a rotating space station
  • · Replies 1 ·
Replies
1
Views
3K
How Does a Rotating Space Station Simulate Gravity for Astronauts?
  • · Replies 1 ·
Replies
1
Views
4K
Circular Motion Questions (energies, forces, angular velocities, etc.)
  • · Replies 2 ·
Replies
2
Views
2K
2 astronauts near a space station (no rotation)
  • · Replies 1 ·
Replies
1
Views
2K
Induced EMF and current for a bar sliding on a circular rail
  • · Replies 22 ·
Replies
22
Views
3K
Finding the radius of the satellite's circular orbit
  • · Replies 3 ·
Replies
3
Views
2K
How Does Apparent Weight Change for an Astronaut Near the Moon?
  • · Replies 5 ·
Replies
5
Views
3K
Difference in Radius of Charged Particles in Magnetic Field
  • · Replies 12 ·
Replies
12
Views
7K
Circular Motion of a Cyclist and a Car going around a bend in the road
  • · Replies 6 ·
Replies
6
Views
4K
Calculating Induced EMF in a Circular Region with Decreasing Magnetic Field
  • · Replies 18 ·
Replies
18
Views
2K