MHB How Does Air Resistance Affect Power in Rotational Motion?

AI Thread Summary
The discussion focuses on calculating the power provided by air resistance to a rotating sphere system after 167 seconds. The sphere, with a mass of 1.9 kg and radius of 0.5 m, is initially rotating at 422 revolutions per minute. After introducing air resistance, which exerts a force of 0.23 N, the calculations involve determining the moment of inertia and angular acceleration. The resulting power calculated is approximately 11.47 W, but there is confusion regarding the correct application of the power formula. The user seeks clarification on their calculations and the correct approach to finding power in this context.
cbarker1
Gold Member
MHB
Messages
345
Reaction score
23
A sphere of mass 1.9 kg and radius 0.5 m is attached to the end of a massless rod of length 3.0 m. The rod rotates about an axis that is at the opposite end of the sphere (see below). The system rotates horizontally about the axis at a constant 422 rev/min. After rotating at this angular speed in a vacuum, air resistance is introduced and provides a force 0.23 N on the sphere opposite to the direction of motion. What is the power (in W) provided by air resistance to the system 167.0 s after air resistance is introduced? (Enter the magnitude.)
10-8-p-102.png


Work
$$I_(new)=2/5mR^2+M(3.5)^2$$= 23.465
$$3.5F_f=I\alpha$$=.034306
$$\alpha=3.5F_f/I$$
$$\omega_0=2\pi/60*422rpm$$=44.19
$$\omega=\omega_0+\alpha*167$$=49.878
$$P=F_f*\omega$$=11.4719

What did I done wrong? Thanks
 
Last edited:
Mathematics news on Phys.org
$P = \tau \cdot \omega$
 
Seemingly by some mathematical coincidence, a hexagon of sides 2,2,7,7, 11, and 11 can be inscribed in a circle of radius 7. The other day I saw a math problem on line, which they said came from a Polish Olympiad, where you compute the length x of the 3rd side which is the same as the radius, so that the sides of length 2,x, and 11 are inscribed on the arc of a semi-circle. The law of cosines applied twice gives the answer for x of exactly 7, but the arithmetic is so complex that the...
Thread 'Imaginary Pythagoras'
I posted this in the Lame Math thread, but it's got me thinking. Is there any validity to this? Or is it really just a mathematical trick? Naively, I see that i2 + plus 12 does equal zero2. But does this have a meaning? I know one can treat the imaginary number line as just another axis like the reals, but does that mean this does represent a triangle in the complex plane with a hypotenuse of length zero? Ibix offered a rendering of the diagram using what I assume is matrix* notation...
Fermat's Last Theorem has long been one of the most famous mathematical problems, and is now one of the most famous theorems. It simply states that the equation $$ a^n+b^n=c^n $$ has no solutions with positive integers if ##n>2.## It was named after Pierre de Fermat (1607-1665). The problem itself stems from the book Arithmetica by Diophantus of Alexandria. It gained popularity because Fermat noted in his copy "Cubum autem in duos cubos, aut quadratoquadratum in duos quadratoquadratos, et...
Back
Top