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Each of the space shuttle’s main engines is fed liquid hydro- gen by a high-pressure pump. Turbine blades inside the pump rotate at 617 rev/s. A point on one of the blades traces out a circle with a radius of 0.020 m as the blade rotates. (a) What is the magnitude of the centripetal acceleration that the blade must sustain at this point? (b) Express this acceleration as a multiple of $g=9.80 \mathrm{m} / \mathrm{s}^{2}$.

$=3.110^{4} \mathrm{~g}$

Physics 101 Mechanics

Chapter 5

Dynamics of Uniform Circular Motion

Newton's Laws of Motion

Applying Newton's Laws

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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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in this problem, we have to find the centripetal acceleration on a on a blade of an engine that is rotating with a given frequency and radius. So not the equation for angular acceleration is vey swear over. Our were not given me in this problem, but we do know a relationship between V and frequency frequency is equal to the over two pi r and if you're confused by that, that comes from the fact that frequency is equal to omega over to pie. Now we can rearrange that to solve for V, which is unequal to F times two pi R that gets plugged back in to our first equation. And now we have everything in terms of giving quantities. So the is equal 22 squared pi squared R to F squared, which is equal to four pi squared times 0.2 times 617 squared. And that is equal to three times 10 to the fifth meters per second. Which is the answer to part a of our problem. Never part beat. We have defined that acceleration in terms of the gravitational acceleration G. Now this is really easy to do all that we need to know is what the value of G is, which is 9.8 meters per second squared. Oh, it's And I just remembered that for here, this primitive second squared. This is an acceleration. Always remember to keep track of your units. So now we do, in fact, have the same units here, which means that we'll get a unit list number, which is correct for a fraction. So when we do it, this math, we get that this value is equal to about three 0.1 times 10 to the fore times G. And that is going with the relation between these two, which is the answer to Part B, and we've solved the problem.

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