SOLUTION: A large wheel and smaller wheel interlocking .The smaller wheel radius 5.23 cm and large wheel radius 8.16 cm.The rotation of the smaller wheel causes the larger wheel to rotate.

Question 349565: A large wheel and smaller wheel interlocking .The smaller wheel radius 5.23 cm and large wheel radius 8.16 cm.The rotation of the smaller wheel causes the larger wheel to rotate. Through how many degrees will the larger wheel rotate if the smaller one rotates through 60.0 degrees ?

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
smaller wheel radius = 5.23 cm.
larger wheel radius = 8.16 cm.

circumference of smaller wheel = 2*pi*5.23 = 32.86105916 cm.
circumference of larger wheel = 2*pi*81.16 = 51.27079211 cm.

for each revolution of the smaller wheel, the larger wheel will go through .640931373 of a revolution.

when the smaller wheel rotates 60 degrees, it has rotated 1/6 of its circumference.

32.86105916 / 6 = 5.4767843193 cm.

the circumference of the larger wheel will have moved the same distance.

5.4767843193 / 51.27079211 = .106821895 which means that the larger wheel has moved through 1.06821895 of its circumference.

that would be equal to approximately 360 * .106821895 = 38.45588235 degrees.

since the number of degrees the wheel turns is equivalent to the proportion of the circumference that it moves, then you can shorten this equation to become the ratio of the circumference of the smaller wheel to the circumference of the larger wheel.

that ratio is equal to 32.86105916 / 51.27079211 = .640931373.

if the smaller wheel moves through a rotation of 60 degrees, then the larger wheel move through a rotation of .640931373 * 60 = 38.45588235 degrees.

60 degree rotation in the smaller wheel = 60 / 360 * 32.86105916 = 5.476843193.

38.45588235 degree rotation in the larger wheel = 38.45588235 / 360 * 51.27079211 = 5.476843193.

concepts:

circumference of circle = 2 * pi * r

length of arc of circle = degrees of rotation / 360 * 2 * pi * r

full rotation = 360 / 360 * 2 * pi * r = circumference of the circle.

wheels interlocking means a movement of the circumference of the smaller wheel is exactly equal to the movement of the circumference of the larger wheel.

the movement is the same in both wheels, but the proportion of movement in each wheel is different.

to see clearer, let the circumference in the smaller wheel be 6 and the circumference in the larger wheel = 12.

they are interlocking.

the smaller wheel rotates through 360 degrees.

circumference of smaller wheel moves 6 which is one complete rotation of the smaller wheel.

circumference of larger wheel also moves 6 only this is only 1/2 the complete rotation of the larger wheel.

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