Question on circular motion involving astronauts and g force?

[Tangeton]

The question is: If an astronaut who can physically withstand acceleration up to 9 times that of free fall (9g) is being rotated in an arm of length 5.0m what is the maximum number of revolutions per second permissible.

I approached this by considering 9g to be the centripetal acceleration (because as there is no other acceleration in circular motion).

I've worked out the time for one revolution many times, but I don't know how to do this the other way around. What equations should I use?

I know I haven't fallowed the strict guide to homework questions but I don't know the equations I could use other than that for centripetal acceleration, a = v^2/r, but that doesn't tell me anything about the maximum number of revolutions per second.

Can someone push me in the right direction for the start? I just look at the question and all equations related to circular motion and just nothing comes to my head.

 

[Doc Al]

The time of one revolution is the period (usually symbolized by T) and you want the frequency. How are period and frequency related?

 

[Tangeton]

The time of one revolution is the period (usually symbolized by T) and you want the frequency. How are period and frequency related?

Oh frequency... F = 1/T. I do remember working out the Time T but I don't know if I was right about how I done it. I used the acceleration and so a = v²/r, 9g = v²/r. I then used this to find the v, v = sqrt of 9gr = 21ms^-1 . And so now I guess I can work out the time T using v = 2∏r/T so T = 2∏r/v = (2∏ x 5.0)/21 = 10∏/21 = 1.50 s.

So F = 1/T = 1/ 1.50 = 0.67 (2sf), is this correct?

EDIT: Is 0.67Hz the final answer? Should I just say it needs to be less than 0.67 of a turn per second?

 

[Doc Al]

Looks good. Express like they asked: The maximum number of revolutions per sec is 0.67.

 

[HalfLostAndSearching]

I would approach this question by first considering the physical limitations and safety concerns for the astronaut. While it is true that they can withstand 9g of acceleration, it is important to note that this is not a sustainable level of acceleration for long periods of time. Therefore, we should aim for a lower number of revolutions per second to ensure the safety and well-being of the astronaut.

Next, we can use the equation for centripetal acceleration, a = v^2/r, to calculate the maximum velocity that the astronaut can safely withstand while being rotated in the arm. We can then use this velocity to calculate the maximum number of revolutions per second using the equation v = 2πr/T, where T is the time for one revolution.

It is also important to consider the length of the arm and the radius of the circular path the astronaut will be traveling in. If the length of the arm is too short, the radius of the path will be smaller and the centripetal acceleration will be greater, potentially exceeding the 9g limit. Therefore, the length of the arm should also be taken into account when determining the maximum number of revolutions per second.

Additionally, we should also consider the effects of angular velocity on the astronaut's body. Rapid changes in angular velocity can cause disorientation and discomfort for the astronaut, so it is important to keep the revolutions per second at a manageable level for their well-being.

In summary, the maximum number of revolutions per second permissible for an astronaut being rotated in an arm of length 5.0m and withstanding up to 9g of acceleration would depend on the physical limitations and safety concerns for the astronaut, as well as the calculations of the centripetal acceleration and angular velocity. It is important to prioritize the safety and well-being of the astronaut while considering the equations and physical principles of circular motion.