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$\cdot$ A model of a helicopter rotor has four blades, each 3.40 $\mathrm{m}$ in length from the central shaft to the tip of the blade. The model is rotated in a wind tunnel at 550 rev/min. (a) What is the linear speed, in $\mathrm{m} / \mathrm{s}$ , of the blade tip? (b) What is the radial acceleration of the blade tip, expressed as a multiple of the acceleration $g$ due to gravity?

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(a) $v=195.8 \mathrm{m} / \mathrm{s}$(b) $a_{\text {rad}}=1.15 \times 10^{3} \mathrm{g}$

Physics 101 Mechanics

Chapter 3

Motion in a Plane

Physics Basics

Motion Along a Straight Line

Motion in 2d or 3d

Newton's Laws of Motion

Cornell University

Rutgers, The State University of New Jersey

Hope College

University of Winnipeg

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.

04:16

In mathematics, a proof is a sequence of statements given to explain how a conclusion is derived from premises known or assumed to be true. The proof attempts to demonstrate that the conclusion is a logical consequence of the premises, and is one of the most important goals of mathematics.

02:50

A model of a helicopter ro…

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03:09

HW2.4 A model of a helicop…

03:21

05:55

A helicopter rotor blade c…

01:55

Helicopter blades withstan…

02:41

02:04

An airplane propeller with…

02:00

(II) A helicopter rotor bl…

02:08

The blades of a fan runnin…

02:14

Helicopter Blades Each of…

01:36

A helicopter has two blade…

So we want to find the linear speed of the blade tip and then the radio acceleration of the blade. So we can say that the radius of the blade or the length of the blade will be 3.40 meters and we can say that the blades are making 550 revolutions per minute. We can convert this into radiance per second. Say to pi, radiance for everyone Revolution. And then for every one minute there are 60 seconds, So divide by 60 seconds and we're getting 57.6 radiance per second. At this point, we can say for part a, the linear velocity will be equal to omega. Times are, though, the angular velocity times the radius. So this will be 6 57.6 times 3.40 and this is equaling 195.8 meters per second. Excuse me for part B, the radial acceleration will equal V squared over R. And so this is get simply going to be equal to the linear velocity squared 195.8 squared, divided by the radius of 3.4. And we're getting thes radio acceleration of the blade equaling 11,276 meters per second squared. Let's go if you wanted to express this and jeez, we can say that a radiant divided by G would simply be 11,276 divided by 9.8 and this would give us 1,151 cheese. So this would be our radio acceleration expressed in insp. Rest in a number of gravity is so like 11 1 1,001 151 times the acceleration due to gravity and then here simply meters per second squared SA units best the end of the solution. Thank you for watching.

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