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

current flows in a wire

Answer from: Quest

the small 0.38-kg slider is known to move from position a to position b along the vertical-plane slot. determine (a) the work done on the body by its weight and (b) the work done on the body by the spring. the distance r = 0.70 m, the spring modulus k = 154 n/m, and the unstretched length of the spring is 0.53 m

explanation:

-reverse card

Another question on Physics

Physics, 22.06.2019 02:00

In which of the following cases is work being done on an object? question 2 options: pushing against a locked door carrying a box down a corridor pulling a trailer up a hill suspending a heavy weight with a strong chain

Answers: 2

Answer

Physics, 22.06.2019 06:00

When you push downward on a book at rest on a table, you feel an upward force. does this force depend on friction? defend your answer.

Answers: 2

Answer

Physics, 22.06.2019 09:30

The graph represents the distance a car travels over time while on the highway. which statement about the car's trip is accurate? a) the car does not move over time. b) the car travels at a constant velocity. c) the car's velocity increases constantly over time. d) the car's velocity decreases constantly over time.

Answers: 1

Answer

Physics, 22.06.2019 10:00

This is important 1. what happens to the speed of molecules in water vapor when it condenses to form a liquid? (2 points) the molecules slow down. the molecules speed up. the molecules slow down and then speed up. the molecules speed up and then slow down. 2. how might human activities change to compensate for a decrease in water supplies? (2 points) humans might build a factory. humans might build drainage systems. humans might extract more water from the ground. human behavior does not change because of the water cycle. i'll be grateful if anyone can answer these 2 questions !

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