If a wheel completes exactly 5 revolutions while rolling 80pi feet, what is the diameter of the wheel?
961901
2 pi = 1 revolution\n80/5 = 16 pi\nC = pi D\n16 pi = D pi\n16= D
1122895
First you find the centripetal acceleration by:\n\na = v^2/r\n\nThen you take that answer and divde by the acceleration due to gravity.  \n\nFor example, let's say the radius of the circle is 10 feet, and the speed is 20 ft/s.  \n\na = 20^2/10 = 40.\n\nThen using 32 ft/s^2 for g you have:\n\n40/32 = 1.25 g's of force.
26747
ok.  call the downward translational velocity of the whole thing v.  this means that the tangential velocity at the edge of the poles (at the radius r) is equal to v.  the reason for this is that the strings are wound AROUND THE POLES, so this winding and the condition that the string has to unwrap for the thing to move, sets the angular velocity w = v/r.\n\nnow, if you look at the main wheel part, the angular velocity has to be equal to the angular velocity of the poles, since they are one solid piece.  however, as you note the radius of the wheel R > r.  so, the fact that v / r = w = V / R implies that V > v.  in other words, the motion of the outer edges of the wheel is faster than the motion of the outer edges of the rods.\n\ni think you are getting confused by saying that V is the translational velocity of the wheel.  it's not.  v is the translational velocity of the wheel, and of the rods.  the fact that the string is wound *around the rods* and not around the wheel sets the angular velocity of the whole apparatus equal to v/r.  V, the tangential velocity of the outer edges of the wheel, is much faster than the translational velocity.\n\nthat clear?
1831
Easiest convertor is just Google -- what a great tip someone showed me!\n\nJust go to google and type in\n  55 ft lbs in newton meters\nand up pops the answer:\n  55 (ft lbs) = 74.5699872 newton meters\n\nLikewise\n  65 (ft lbs) = 88.1281666 newton meters\n\nAnd\n  75 (ft lbs) = 101.686346 newton meters\n\nTo give you an idea of what this means, a standard mechanics torque wrench can apply up to 200 newton meters of turning force.
870230
This is one of those look hard but not really math riddles. The answer is actually 1800 degrees. Also known as a five full spin turn. Where will it be? You just leave it there!\n\n1440 is 4 full spins. But that under 1441 so go to the next full spin, 1800 degrees. 1800 is between 1441 and 1892 so that's the answer.\n\nI can't actually think any other easier spin than a full spin. You don't have to move or rotate it at all. You just leave it in it's original spot.
908729
(a) ω = ωo + αt\n0 = 150 + α * 132\nα = -150/132\n≈ -1.136 rev/s²\n\n(b) θ = ωot + ½αt²\n= 150 *132 - ½*1.136*132²\n≈ 9903 revolutions (nearest rev)\n\n(c) See (b)\n\n(d) 75 rpm = 75*2π rad/min\nα = rω²\n= 50 *(75*2π)²\n≈ 11103300 cm/min²\n= 111033 m/min²\n= 111033/3600 m/s²\n≈ 30.84 m/s²\n\n(e) ???? I do not understand what it is you are seeking.
894020
Here's a method to measure pi.  You'll need a greasy marker, a wheel, and a flat surface to roll it on.\n\nMark a spot on the wheel with the marker.\n\nRoll the wheel on the floor long enough for the mark on the wheel will make two marks on the floor.\n\nMeasure the distance between the two marks on the floor - that's the circumference of the wheel.\n\nMeasure the diameter of the wheel.\n\nPi is the ratio between the circumference and the diameter.  Voilà!  Of course, this is subject to measurement error but you should get a pretty good approximation.
939877
E=kinetic energy of wheel\nr= radius of wheel\nw=angular speed of wheel\nm=mass of wheel\nT=required torque\nt=stopping time \nW=necessary work to stop the wheel = E\n\nE=m r^2 w^2\nW=T * (w+0)/2 * t\nE=W\nT=2mw r^2/t\nT=10.77 N.m
727926
88 revolutions per 5 seconds = 88/5 rps = 17.6 rps (revolutions per second) or in rpm...\n=  88*60/5 rpm = 1056 rpm (revolutions per minute).
525309
1) Convert rpm to revolutions per second, by dividing rpm by seconds (so the minutes cancel).\n\n2)Convert revs per sec to radians per second, by multiplying rev/sec *2pi rad/rev (the revs cancel).\n\n3 Acceleration is in the form of distance/(time^2), so dividing radians per second by the time required to stop will give you the magnitude of acceleration over that time period. \n\nFor your example:\n\nrotational acceleration = \n            1000 rev/min *1 min/60 sec* 2Pi rad/rev *1/2 sec\n           =  52.4 rad/sec^2\n                 \n\nPart 2:"\n\nIf by distance you mean radial distance traveled by the tip of a spinning blade, then you know that \n\n1 revolution = 2*pi*r \n\nso to find the number of revolutions, multiply the distance by 1 rev/(2*pi*r)- the units of linear distance will cancel (see a pattern?).\n\n(distance) * 1rev/(2*pi*r) = number of revolutions
1053261
70cm hieght of the topstep\n4 degree angle off the ground\n\na) 70/(sin 4*) = 1003 cm or 10.03 m\n\nb) arcsin times 70/900 = 4.46* \n\nyes it will meet wheel chair code
932723
This is a classic conservation of angular momentum question.\nWe will assume frictionless motion.\nThe angular momentum is always:\n\n1/2 r^2 m  for the disk\nplus\nd^2 m for the man\nthe sum multiplied by the angular speed\n\nsince the momentum is conserved:\n\n(1/2*4*25+85*4)*.15=\n(1/2*4*25+85*.7^2) speed\n\nspeed=.64 rev/s\n\nI'll let you convert it to radians per second\n\nj
725445
You can't without the radius of the wheel...m/s is a tangential speed.
333495
The scale would tell you that.  For example a hot wheels car is 1:64 so 1 inch on the hot wheel is 64 inches on the real car.
748663
The answer hippoterr... gave you was OK till the last step. It's always is wise to check the units and see if they make sense. His result is in sec/rev.\n\n2 x Pi x11.5 / 30 = 2.4 He left out the units in the math part, but if you include them you see that the result is in sec/rev.\n\nUnit conversion can be confusing. A better way - you know you want it to be something per sec so start with:\n\n30 meter/sec. Then to convert to rev/sec multiply by 1, in a special form.\n\nIn the form 1 rev/(2 x Pi x11.5 meters). This = 1, right? The top and bottom are equivalent. So back to \n\n30 meter/sec * 1 rev/(2 x Pi x11.5 meters) = .415 rev/sec\n\nYou understand why weight/mass wasn't needed? It's the acceleration that results from the rotation,  and  a = F/m.
970150
We calculate in radians for convenience.\n\nFixed part of rotation from initial v is\n48 * 7 = 336\n\nVariable part from additional acceleration is\nd = 1/2 a t^2\nwhere acceleration a is\n(120 - 48) / 7 = 10.3 r/sec^2\ntherefore d is\nd = 1/2 * 10.3 * 7 * 7 \nd = 252\n\nTotal d is then\n252 + 336 = 588 radians\nand total revolutions is 588 / (2*pi) = 93.6
1060039
so that they roll. why are wheels round?