1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
alex41 [277]
3 years ago
5

A girl (mass M) standing on the edge of a frictionless merry-go-round (radius R, rotational inertia I) that is not moving. She t

hrows a rock (mass m) in a horizontal direction that is tangent to the outer edge of the merry-go-round. The speed of the rock, relative to the ground, is v. Calculate (a) the angular speed of the merry-go- round and (b) the linear speed of the girl after the rock is thrown.
Physics
1 answer:
vladimir1956 [14]3 years ago
5 0

a) \omega=\frac{-mvR}{I+MR^2}

b) v=\frac{-mvR^2}{I+MR^2}

Explanation:

a)

Since there are no external torques acting on the system, the total angular momentum must remain constant.

At the beginning, the merry-go-round and the girl are at rest, so the initial angular momentum is zero:

L_1=0

Later, after the girl throws the rock, the angular momentum will be:

L_2=(I_M+I_g)\omega +L_r

where:

I is the moment of inertia of the merry-go-round

I_g=MR^2 is the moment of inertia of the girl, where

M is the mass of the girl

R is the distance of the girl from the axis of rotation

\omega is the angular speed of the merry-go-round and the girl

L_r=mvR is the angular momentum of the rock, where

m is the mass of the rock

v is its velocity

Since the total angular momentum is conserved,

L_1=L_2

So we find:

0=(I+I_g)\omega +mvR\\\omega=\frac{-mvR}{I+MR^2}

And the negative sign indicates that the disk rotates in the direction opposite to the motion of the rock.

b)

The linear speed of a body in rotational motion is given by

v=\omega r

where

\omega is the angular speed

r is the distance of the body from the axis of rotation

In this problem, for the girl, we have:

\omega=\frac{-mvR}{I+MR^2} is the angular speed

r=R is the distance of the girl from the axis of rotation

Therefore, her linear speed is:

v=\omega R=\frac{-mvR^2}{I+MR^2}

You might be interested in
HELP!! ME pls which Which of the following graphs correctly shows the relationship between KE and VELOCITY? *
faltersainse [42]

Answer: Option 3.

Explanation:

Formula for kinetic energy is

K.E = (1 / 2) * (m * v ^ 2)

Assuming mass to be constant,

We can see that K.E is proportional to v^2.

It means that when you substitute the value of velocity in v, kinetic energy increases with v^2.

Option 1 and 2 are eliminated because the relationship between kinetic energy and velocity in the graph is shown as linear. We already know from formula that the relationship is not linear.

Option 4 is incorrect because kinetic energy must be zero when velocity is zero. This graph shows kinetic energy is becoming infinite as velocity tends to 0.

So option 3 is correct answer.

3 0
3 years ago
Please need help on this
Vera_Pavlovna [14]

Answer:

i have no idea

Explanation:

it could be B. but i dont belive in myself sooooooooooo.....ehhhh yeah

4 0
3 years ago
What is the electric potential of a 2.2 µC charge at a distance of 6.3 m from the charge? Recall that Coulomb’s constant is k =
Doss [256]
The first part of the question is 3,100 V.

The second part of the question is 200 V.
6 0
3 years ago
Read 2 more answers
What is a speed of a car if it covers 130 km in 2 hours?
inysia [295]

Answer:

65 km per hour

Explanation:

130/2=65

3 0
3 years ago
Read 2 more answers
A train 471 m long is moving on a straight track with a speed of 75.1 km/h. The engineer applies the brakes at a crossing, and l
hram777 [196]

Answer:

t = 37.6 s

Explanation:

As we know that train is initially moving with the speed

v_i = 75.1 km/h

now we know that

v_i = 20.86 m/s

now the final speed of the train when it crossed the crossing

v_f = 15 km/h

v_f = 4.17 m/s

now we can use kinematics here

v_f^2 - v_i^2 = 2 a d

4.17^2 - 20.86^2 = 2 a(471)

a = -0.44 m/s^2

Now the time to cross that junction is given as

v_f - v_i = at

4.17 - 20.86 = a(-0.44)

t = 37.6 s

4 0
2 years ago
Other questions:
  • Scientists can estimate the age of a planetary surface by counting __________. scientists can estimate the age of a planetary su
    15·1 answer
  • What is the speed of a 0.145kg baseball if its kinetic energy is 109J?
    15·1 answer
  • What is the product of mass and velocity of an object?
    5·2 answers
  • Why is the sun renewable but oil is non renewable?
    15·1 answer
  • Can someone please help me on this!!!
    15·1 answer
  • 1. How are science and technology related? (1 point)
    6·1 answer
  • Explain the amount of chromosomes and gene combinations in a parent cell and offspring that result from meiosis and fertilizatio
    14·1 answer
  • Whichiscorrect?(A)anopaqueobjectdoesnotallowlighttopassthroughit.(B)an
    7·2 answers
  • The chemical equation for the decomposition of potassium chlorate into potassium chloride and oxygen gas is
    13·1 answer
  • 30 kg sits on a table the acceleration due to gravity is 10 m/s^2 what force does the table exert on the television.
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!