rolling coin
Two identical Re1 coins are kept on a table touching each other as shown in the figure below. One of the coins is fixed on the table whereas the other coin rolls (without sliding) along the periphery of the fixed coins, touching it all times. How many complete rotations has the rolling coin made, when it reaches its initial position again for the first time?
a. 1
b. between 1 and 2
c. 2
d. between 2 and 3
e. 3
No Dr !!!
It should be c. 2
The rolling coin is covering a distance of 2π(2r) where r is the radius of each coin
and the distance covered by a coin in one rotation is 2πr
So number of rotations = 2
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but, i guess that's the center of the rolling coin which is at a radius of 2r.. we have to find out how much a point on the periphery of the rolling coin moves.. the total distance covered by the coin in one rotation is 2?r.. and that's exactly how much the point touching the static coin moves... hence, the coin goes for one rotation..
you can even check it experimentally..
give ur comments..
It's the center of the rolling coing coin which is at a distance of 2r from the center of the static coin.. to find out how many rotations a coin make, we calculate how much the a point on periphery has moved not how much the center has moved.. the distance covered by any point on periphery= 2πr. hence the no. of rotations made by the rolling coin=1.
this can be even checked experimentally...
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Though if u do it appears as 1....Bt the two coins togedr is used as a whole system whose radius is 2r..
So reqd nswer is 4*pi*r/2*pi*r=2.....
So option (c) is correct one....
Giv ur best to d world.
Nd d best will cm back to u.....
Regards,
Dipanjan......
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It's the center of the rolling coing coin which is at a distance of 2r from the center of the static coin.. to find out how many rotations a coin make, we calculate how much the a point on periphery has moved not how much the center has moved..
are you sure???
I guess its the other way around.
we always calcualte how much the center has moved
and in thz questions the center is moving a distance 4(pi)r. . so the number of rotations is
2
no. of rotations will be one, still.
dude... now lets look at the question once..
"one of the coins is fixed at the table... and the other coin is being rotated around it.."
now look at this way..
the static coin is just providing a path for the rolling coin to traverse.. in other ways, the static coin is as good as any flat path..
one more thing.. you must have noticed, the static coin is fixed and the rolling coin has to move around it.. so one thing is for sure, the coins are placed with one of their faces lying on the table..
so, if u now consider the motion of the rolling coin, it just traverses a path 2(pi)r long.. it doesn't make any difference if the path is flat or not..
the no. of rotations would have been different if the static coin also moved.. but, that's not so..
FINALLY, TELL ME JUST A THING.. IF A CYCLE MOVES ON A ROAD, FOR A DISTANCE 2(PI)R TRAVELLED BY THE CYCLE, WHERE R IS THE RADIUS OF THE WHEEL, IS THE NO. ROTATIONS DIFFERENT IF THE ROAD IS FLAT OR NOT?? NO.. THEY ARE ALWAYS THE SAME. ...
ps. try to do this experimentally.. better, still draw the motion of the coin.. it will be clear...
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we would have considered how far is center, iff the static coin was also moving.. otherwise, no..
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ans -option (a) do practically
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