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Multiple-Concept Example 13 offers a helpful perspective for this problem. Suppose the surface (radius r) of the space station in Figure 5.18 is rotating at 35.8 m/s. What must be the value of r for the astronauts to weigh one-half of their earth-weight?

262$m$

Physics 101 Mechanics

Chapter 5

Dynamics of Uniform Circular Motion

Newton's Laws of Motion

Applying Newton's Laws

Rutgers, The State University of New Jersey

University of Michigan - Ann Arbor

University of Washington

Lectures

03:28

Newton's Laws of Motion are three physical laws that, laid the foundation for classical mechanics. They describe the relationship between a body and the forces acting upon it, and its motion in response to those forces. These three laws have been expressed in several ways, over nearly three centuries, and can be summarised as follows: In his 1687 "Philosophiæ Naturalis Principia Mathematica" ("Mathematical Principles of Natural Philosophy"), Isaac Newton set out three laws of motion. The first law defines the force F, the second law defines the mass m, and the third law defines the acceleration a. The first law states that if the net force acting upon a body is zero, its velocity will not change; the second law states that the acceleration of a body is proportional to the net force acting upon it, and the third law states that for every action there is an equal and opposite reaction.

03:43

In physics, dynamics is the branch of physics concerned with the study of forces and their effect on matter, commonly in the context of motion. In everyday usage, "dynamics" usually refers to a set of laws that describe the motion of bodies under the action of a system of forces. The motion of a body is described by its position and its velocity as the time value varies. The science of dynamics can be subdivided into, Dynamics of a rigid body, which deals with the motion of a rigid body in the frame of reference where it is considered to be a rigid body. Dynamics of a continuum, which deals with the motion of a continuous system, in the frame of reference where the system is considered to be a continuum.

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Multiple-Concept Example 1…

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Suppose the surface radiu…

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A space station is in the …

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To find the rotational rat…

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A space station is in the…

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The formula$$N=\frac{1…

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A space station is shaped …

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Consider the circular spac…

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Radius of Earth A spacelab…

in this problem, we have defined the radius required for a rotating space station to allow the astronauts on board to have half of their weight on earth. So what does that actually mean for us? Mathematically? Well, what causes our weight on Earth is, of course, the force of gravity mg. And so if we want that to be half of what it is on Earth, the astronauts mass itself isn't going to change because that's intrinsic toe, uh, their bodies. But we can affect G, since that is, um, acceleration. So we know that we want the the force on the astronauts or the acceleration acting the astronauts rather to be 1/2 of G. All right, so on a rotating space station, assuming that there is no other sorts of gravity, the centripetal force is going to be what causes the astronauts to feel any kind of gravitational force. So that means that M v squared over R is going to you. It's equal to 1/2 mg, so that is just an a our net force canceling at the EMS. We find that we can rewrite the equation for the radius. As to these squared Oh, Fergie on Since we know V squared and juice just a constant, we can now plug in or numbers that were given and solve the problem. Views 35.8 meters per second and G is of course, 9.8 meters per second squared. And when we solve this we find that our is 262 meters. The solution to this problem

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