00:01
Hello everyone here it is given each gear a and b having the mass 2 .4 kg and radius of gyration 60mm that is 0 .06 meter while gear c having the marks 12 kg and radius of chiration 150 m that is 0 .15 meter radius of c is 2 .15 meter radius of c is 2 that is 0 .2 meter and that of a and b is same 80mm that is 0 .08 meters.
01:10
If couple m of constant magnitude of 10 newton is applied to v applied to gear v calculate number of commercial gerti required theta for of c required to increase velocity angular velocity omega 1 100 rpm 450 rpm and v tangential force on a let us see here first up inertia of gear a and b both having the same because both are of same dimension m into k square, mass is 2 .4 kg.
03:07
Radius of variation of each is 0 .06 meters.
03:13
So it will be 8 .64 into 10 to the power minus 3 kg meter square.
03:20
Moment of inertia of gerc, mass is 12, radius of variation is 0 .15.
03:29
So it would be 270 into 10 to the power minus 3 kg meter square.
03:45
Here it will be r a is called to omega a is called to r v is called to omega v is called to omega v is called to r c into omega c.
03:56
This condition to be satisfied.
04:03
So omega a is equal to omega v is called to 200 by 80 into omega c that is 2 .5 omega c.
04:18
And we can write angular displacement of a, theta a, is equal to theta v, is equal to 2 .5 times of theta c.
04:32
Now, kinetic energy we will calculate by the formula.
04:41
T is called to half i omega squared here.
04:54
Angular velocity of a is called to z of b is 2 .5 times of omega -c.
05:05
Given omega c is equal to 100 rpm that is 10 pi upon 3 radiant per second so angle a and b you will get this is 1 so 1a is equal to 1 b is equal to 1 b is called to 2 .5 times of omega 1c that is 25 pi upon 3 radian per second initial in energy of gear a, how moment of energy up you have to use this relation.
06:08
Moment of inertia we have calculated of each individual gear and angular velocity.
06:20
So even a will be 2 .9690.
06:29
Energy of v will be the same because both having the same dimension still i am writing here both having the same initial kinetic energy.
06:55
Now initial kinetic energy of gerti half.
07:11
Its momentum of energy is 270 and angular velocity is 10x by 3.
07:21
So it would be 14 .8084.
07:27
So total kinetic energy of the system, total initial kinetic energy of the system t, 1 is called to t1a, t1v and t1c substituting the value.
08:17
So t1 we will get 20 .726 jude...