00:01
Hello everyone in the given diagram there are three gear a, b and c.
00:06
Gare a having the weight 1 pound radius of variation 1 .3 inch and radius is 2 inch gear b having the weight 6 pound radius of piracy 3 inch it having two radius inner one is 4 inch and outer is in contact to a radius is r 4 inch and in contact to 3c its radius is 2 inch.
00:35
Gair c having the weight 9 pound radius of variation 4 .3 inch and radius is 6.
00:43
If moment of couple 40 pound inch applied on a then we have to find angular acceleration of c gear and course applied by v on c gear.
00:57
Let us start solving.
00:59
First we will find moment of inertia of each gear.
01:02
Moment of energy of each gear.
01:05
Moment of inertia of a will be mass into square of radius vibration so you know the weight so 1 pound divided by 32 .2 so it becomes mass into radius of variation and the radius of variation is given 1 .3 inch so it has to be taken in 5th so that is 12 square so on solving it its value will be 0 .3 448 into 10 to the power minus 3 pound fit square.
01:50
Similarly radius of variation of v gap it will be 6 upon 32 .2 its radius of variation is 3 so 3 divided by 12 whole square so it would be 11 .646 into 10 to the power of minus 3 pound fit square radius of variation of c will be its weight is given 9 32 .2 into 4 .3 divided by 12 whole square so on solving it it's the value you will get 35 .889 into 10 to 10 to the power minus 3 pound fit square gear a having the radius 2 inch gear b having the radius r1 4 inch and r2 2 inch and gear c having the radius 6 inch since the point of contact of c with point of contact between a and b and having same tangential acceleration so we can write tangential acceleration to be r a alpha a is equal to r v alpha v so from here you may write alpha a to v r v upon r a into alpha v r v is given 4 inch r a given 2 inch into alpha so finally you may write angular acceleration of a is two times angular acceleration of b.
04:53
Similarly, point of contact between b and c having same tangential acceleration.
05:19
So you may write rv alpha v, rc, alpha c.
05:31
So alpha b can be written as rc, c, rc, c.
05:36
Upon r v into alpha c so we can say alpha v r c is given six this is two so you may write alpha v is three times of alpha c or we can also write alpha a is six times of alpha c now we will analyze the motion of gear a, so moment of couple on gear a, this is the gear a, tangential force applied by b on a, say f, va, or you may say fab, that is your choice.
07:08
Couple m is given, it having the value, 40 pound inch square, this is a, so if you calculate moment of couple about a point, considering clockwise to be positive you will write m minus f a v into r a to be i a into alpha a m here you may write 40 into pound you may convert it 40 divided by 12 square pound fatt square f t r a v is given 2 inch so 2 by 12 i a we have measured 0.
08:39
Just a moment please i a we have to see i a is 036 036 10 to the power minus 3 into 6 alpha c so from here you may write force on gear a applied by v to v by solving this equation it can be written as 20 minus 013121 alpha c say this is equation 4 now we will analyze moment of couple on the gear let us see here this is the gear v the v point here it will be f a v this is f vc this this radius we know 4 inch and this is given 2 inch now this direction counter clockbyes we are considering positive submission of moment of force about v we are calculating so it will be f a v r1 minus f vc r2 to be equal to i v v into alpha v so from here f vc force could be written as r1 upon r2 f a v v m minus i v alpha vl v upon r2 now substitute the value of f a b from equation 4 and r1 r2 ratio we know r1 is radius of r1 is 2 sorry 4 this is 2 fab we have measured 20 minus using the equation number 4 0 .013121 alpha c moment of inertia alpha v can be written as three times of alpha c and moment of inertia of v gear is 11 .646 into 10 to the power of minus 3 divided by r2 that is 2 by 12 so on solving it, force on v, yeah, force on a due to b, whatever the symbol you like, whatever i have is that i am writing, it doesn't matter...