A 55 m diameter merry go round is rotating freely with an...

A 5.5 m diameter merry-go-round is rotating freely with an angular velocity of 0.80 rad/s. Its total moment of inertia is 1,900 kg.m2. Four people standing on the ground, each with a mass of 80 kg step on to the edge of the merry go-round. What is the angular velocity of the merry-go-round after the fourth person steps on to it? Provide you answer in radians per second.

Transcript

0:00 Hello.

00:01 So in this question it is given to us that the mass of each person m is equal to 65 kilograms.

00:12 The number of people n is equal to 4.

00:17 The diameter of the murray go round is d is equal to 4 .2 meters.

00:26 So the radius r should be equal to diameter divided by 2 which is equal to 0 .1 meters.

00:34 The angular velocity omega initially is equal to omega i is equal to 0 .8 radiance per second and the moment of inertia i is equal to 1 ,760 kilogrammeatres square.

00:57 Initially so i i initial moment of inertia is equal to 1 ,760 kilogram per meters well so here we will be using the law of conservation of angular momentum to find the final angular velocity so according to the law of conservation of angular momentum the angular momentum sorry the angular momentum l1 is equal to the angular momentum l2, that is the initial angular momentum is always equal to the final angular momentum unless there is an external torque acting on the body.

01:39 So here there is no external torque acting on the body and hence the initial angular momentum l1 must be equal to the final angular momentum l2.

01:49 We know that the initial angular momentum l1 must be equal to the initial moment of inertia i i multiplied by the final sorry the initial angular velocity omega i similarly the final angular momentum should be equal to the final moment of inertia i f multiplied by the final angular velocity omega f now what is the final moment of inertia it is equal to the initial moment of inertia i i plus 4 m r square okay because now four people of mass m each that is 65 kilograms each is standing on the end of this particular rim okay the end of this particular merry go around so what happens is we have to add the moment of inertia for those masses also so that is uh the initial moment of inertia plus 4mr square.

02:57 Okay, now substituting the values we can write 1 ,760 multiplied by 0 .8 is equal to 1 ,760 plus 4 multiplied by 65 multiplied by 2 .1 square.

03:23 The whole multiplied by what is the value of omega f that we need to find out...

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