Physics, 08.04.2020 02:54 heroxtree

A merry-go-round rotates at the rate of 0.14 rev/s with an 84 kg man standing at a point 2.4 m from the axis of rotation. What is the new angular speed when the man walks to a point 0 m from the center

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Answer from: Leigh305

The given question is incomplete. The complete question is as follows.

A merry-go-round rotates at the rate of 0.14 rev/s with an 84 kg man standing at a point 2.4 m from the axis of rotation. What is the new angular speed when the man walks to a point 0.6 m from the center? Assume that the merry-go-round is a solid 25-kg cylinder of radius 2.0 m.

Explanation:

The given data is as follows.

Initial angular velocity ( $\omega_{1}$ ) = 0.14 rev/s

$\omega_{1} = (0.14 \times 2 \pi) rad/s$

= 0.87 rad/s

Mass of man (M) = 84 kg, Mass of cylinder (m) = 25 kg

Radius of the cylinder (r) = 2.4 m

Let $r_{1}$ be the initial distance of man from the axis of rotation = 2.0 m

Final distance of man from the axis of rotation ( $r_{2}$ ) = 0.6 m

Formula to calculate the moment of inertia of cylinder is as follows.

I = $\frac{Mr^{2}}{2}$

And, moment of inertia of man = $mr^{2}$

Therefore, initial moment of inertia of the system is as follows.

$I_{1} = \frac{Mr^{2}}{2} + mr^{2}_{1}$

= $\frac{84 \times (2.4 m)^{2}}{2} + 25 \times (2)^{2}$

= 241.92 + 100

= 341.92 $kg m^{2}$

Now, final moment of inertia of the system will be calculated as follows.

$I_{2} = \frac{Mr^{2}}{2} + mr^{2}_{2}$

= $\frac{84 \times (2.4)^{2}}{2} + 25 \times (0.6)^{2}$

= 241.92 + 9

= 250.92

Now, according to the law of conservation of angular momentum is as follows.

Initial angular momentum = Final angular momentum

$I_{1} \omega_{1} = I_{2} \omega_{2}$

or, $\omega_{2} = \frac{I_{1}\omega_{1}}{I_{2}}$

= $\frac{341.92 \times 0.87}{250.92}$

= 1.18 rad/s

Thus, we can conclude that the new angular speed is 1.18 rad/s.

Answer from: Quest

the minimum amperage that the current in this wire would have to have so that its weight is completely supported by the magnetic force due to earth's field, assuming that no other forces except gravity act on it

Answer from: Quest

i had this question and the answer was 3.15 miles.

martina travels from school to her mom's office. from there, she walks to school. after school, she walks to the library and then to a friends house before finally ending back at home. find martina's total distance traveled.

a) 0 miles

b) 0.4 miles

c) 1 mile

d) 3.15 miles

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A merry-go-round rotates at the rate of 0.14 rev/s with an 84 kg man standing at a point 2.4 m from...

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