physics angular velocity question..help please!?

Question

someone sits on a rotating stool and rotates at 30 rev/min while holding 10kg mass in each outstretched arm. The moment of inertia of the person plus the stool is 5 kg.m² and is considered constant. the two masses initially rotate at a radius of 1.0m but then the arms are folded to .15m. what is the new angular velocity of the system (in rev/min)??

Answer 1

In the beginning, was the total moment of inertia, MI1; and I saw MI1, and it was good. Not only was it good, but it was given by:

MI1 = 5.0kg m^2 + 2 (10)(1)^2 kg m^2 = (5 + 20) kg m^2
= 25 kg m^2.

But then arms were folded, and lo: there was a lower moment of inertia. And amid the gnashing of teeth and the renting of garments, the moment of inertia was found to be:

MI2 = 5.0kg m^2 + 2 (10) (0.15)^2kg m^2 = (5 + 0.45)
or 5.45kg m^2.

But the angular momentum was conserved, i.e. MI1 w1
= MI2 w2;

thus 25.0 w1 = 5.45 w2, so that w2 = (25.0/5.45) 30 rev/min

= 137.6... rev/min.

A dizzying conclusion !

Live long and prosper.

Answer 2

The total angular inertia is the sum of the angular inertia of the person, stool and weights.  The sum of the first two is given, so you only need to figure the last.

Configuration 1:
I1 = 5.0 + 2 * (10 kg * (1 m)^2)

Configuration 2:
I2 = 5.0 + 2 * (10 kg * (0.15 m)^2)

You also have conservation of angular momentum:

I1ω1 = I2ω2

Or, ω2/ω1 = I1/I2

I'll let you plug in the numbers.

Answer 3

angular velocity = angular displacement/time on account that physique reaches diametrically opposite ingredient as a result, perspective or angular displacement is 180degree or pi radian so, angular velocity = pi/2 = a hundred and eighty/2 = ninety/sec and linear velocity = displacement/time = 7/2 = 3.5m/s