Physics is way harder than Math.. More problems....?

Question

A model of a helicopter rotor has four blades, each 3.60 m in length from the central shaft to the blade tip. The model is rotated in a wind tunnel at 580 rev/min.

(a) What is the linear speed of the blade tip, in m/s?
_________m/s
(b) What is the radial acceleration of the blade tip expressed as a multiple of the acceleration due to gravity, g?
_________ g

Answer 1

Actually, math is way harder than physics. Physics, at least undergrad and HS physics, deals for the most part in tangible things. Things and events you probably have experienced in one form or another.

Math is just a language, like any other language. So you have to memorize a lots of stuff in math where you can draw on your own experiences in physics. For example...your problem.

a) You've probably ridden on a carousel (merri-go-round). What did you notice about the speeds? On the outside edge of the carousel, where the red stallion can be ridden, the speed is pretty fast. But on the inside, where the music comes from, the speeds are relatively slow.

Yet the carousel is spinning at the same rate of rotation. It has to; otherwise it'd break apart. Well, that rate of spinning is called angular velocity (w) and it is a measure of degrees, radians, revolutions, and such per unit time. In your problem w = 580 rev/min.

If w is the same throughout the carousel, then why are we going faster on the red stallion than inside near the music box? Well, that's because we're farther from the center of rotation on the stallion than near the music. And distance from the center of something circular, like the merri-go-round, is measured along the radius. Thus our speed on the steed V must very according to the distance R from the center. In fact, V = wR because it must clearly vary with the angular velocity as well.

So, back to your problem V = wR = 580 rev/min*3.60 meters; but we have a units problem here. What's rev-meters/min? Well, here comes some of that math you have to memorize (it's not physics), 1 rev = 2pi radians and radians (again not physics) are dimensionless. So V becomes = 580*2pi*3.60 meters/min; change the minutes to seconds and you have your answer.

b) Acceleration along the radius is called centripetal acceleration. And centripetal force is P = mV^2/R; so V^2/R = centripetal (radial) acceleration = a. You worked V above and R is = 3.60 m; so you can find a. Purists will tell you that P is really centrifugal force, but even purer purists will tell you there is no such thing as centrifugal force. What it turns out is that even though it does not exist (really), centrifugal is a faux force that is easier to calculate than the real, centripetal force. So we physicists, being basically lazy, choose to calculate centrifugal force and just call it centripetal but in the opposite direction.

G = number of g's = a/g; the answer you are looking for. g = 9.81 m/sec^2 on Earth's surface.

Answer 2

What the heck are you talking about? Physics IS math, except it is used to calculate real things in this world, whereas math is used to calculate mental problems. Take the Euler's Trail for example. Would you say that there is a physical reason as to why it doesn't work? No, it is the laws of mathematics that makes it so it can't work. But when we talk about why why a frying pan shakes at a very hot temperature, that's physics. There the same thing, just used to calculate different aspects.
Mathematics is the reason our universe even exists. If the number 4 never existed, how can there have been a fourth person on this planet? Please, no religious reasons but seriously, mathematics is physics.