Physics, 06.02.2022 09:20 jaxhat646

A merry-go-round rotates at the rate of 0.2 rev/s with an 88 kg man standing at a
point 2.1 m from the axis of rotation.
What is the new angular speed when the
man walks to a point 0 m from the center?
Consider the merry-go-round is a solid 75 kg
cylinder of radius of 2.1 m.
Answer in units of rad/s.

Answers: 3

Show answers

Answers

Answer from: esmeraldavelez63

So, the new angular speed when the man walks to a point 0 m from the center (in rad/s) is approximately 0.87π rad/s.

Introduction

Hi ! I will help you with this problem. This problem will mostly adopt the principle of rotational dynamics, especially angular momentum. When there is a change in the mass or radius of rotation of an object, it will not affect its angular momentum, only its angular velocity will change. Therefore, the law of conservation of angular momentum can be written as :

$\sf{L_1 = L_2}$

$\sf{I_1 \times \omega_1 = I_2 \times \omega_2}$

$\boxed{\sf{\bold{m_1 \times (r_1)^2 \times \omega_1 = m_2 \times (r_2)^2 \times \omega_2}}}$

With the following condition :

$\sf{m_1}$ = initial mass (kg) $\sf{m_2}$ = final object mass (kg) $\sf{r_1}$ = initial turning radius (m) $\sf{r_2}$ = final turning radius (m) $\sf{\omega_1}$ = initial angular velocity (rad/s) $\sf{\omega_2}$ = final angular velocity (rad/s)Rationale

Previously, we assumed that when rotating, only merry-go-round that experienced inertia so the man will only add to the mass of the merry-go-round. Perhaps, having a man at the end of it will change the slope (direction of torque), but not change the value of angular momentum. So, when this person is in the middle or on the central axis (read: 0 m from the center), the man no longer had any effect on the weight gain.

Problem Solving

We know that :

$\sf{m_1}$ = initial mass = 88 (man) + 75 (object) = 163 kg $\sf{m_2}$ = final object mass = 75 kg $\sf{r_1}$ = $\sf{r_2}$ = r >> The radius of rotation is always the same $\sf{\omega_1}$ = initial angular velocity = 0.2 rev/s = 0.2 × 2π rad/s >> 0.4π rad/s

What was asked :

$\sf{\omega_2}$ = final angular velocity = ... rad/s

Step by step :

$\sf{m_1 \times (r_1)^2 \times \omega_1 = m_2 \times (r_2)^2 \times \omega_2}$

$\sf{163 \times \cancel{(r)^2} \times 0.4 \pi = 75 \times \cancel{(r)^2} \times \omega_2}$

$\sf{65.2 \pi = 75 \times \omega_2}$

$\sf{\omega_2 = \frac{65.2 \pi}{75}}$

$\boxed{\sf{\omega_2 \approx 0.87 \pi \: rad/s}}$

Conclusion

So, the new angular speed when the man walks to a point 0 m from the center (in rad/s) is approximately 0.87π rad/s

Answer from: Quest

the inner core.

good luck: )

klicker

Answer from: Quest

answer: the metamorphic rocks are formed when they are exposed to high pressure and high temperatures. this happens when one of the earth's plates comes in contact with the other plate by traveling in opposite directions, straight into each other or slipping under one another. the friction that is caused by this activity results in melting of rocks and when it cools they are known as metamorphic rocks. this process needs a controlled amount of pressure and temperature otherwise it may turn into magma.

Another question on Physics

Physics, 22.06.2019 02:20

According to newton’s first law of motion, which force is expected to cause a body to accelerate?

Answers: 1

Answer

Physics, 22.06.2019 08:30

An object weigh 40n in air ,weigh 20n when submerged in water,and 30n when submerged in a liquid of unknown liquid density.what is the density of unknown of liquid?

Answers: 1

Answer

Physics, 22.06.2019 16:30

He latent heat of vaporization for ethyl alcohol is 854 j/g. the amount of energy, rounded to the nearest whole number, needed to change 5.20 grams of ethyl alcohol from a liquid to a gas is

Answers: 2

Answer

Physics, 22.06.2019 21:30

Ineed this now one scientist feels that the changes in global climatic patterns may be good for the health of the biosphere. another scientist feels that sharp changes in climatic patterns could result in the extinction of the biosphere. which of these is the most likely reason the two scientists gave conflicting opinions on the impact of changes in the global climatic pattern? they do not have enough knowledge on the topic. they did not discuss the issue among themselves. they believe conflicting opinion strengthens science. they study different areas of science and have different scientific focuses.

Answers: 1

Answer

You know the right answer?

A merry-go-round rotates at the rate of 0.2 rev/s with an 88 kg man standing at a
point 2.1...

Questions