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
IrinaK [193]
3 years ago
15

A wheel is rotating freely at angular speed 660 rev/min on a shaft whose rotational inertia is negligible. A second wheel, initi

ally at rest and with 5 times the rotational inertia of the first, is suddenly coupled to the same shaft. (a) What is the angular speed of the resultant combination of the shaft and two wheels? (b) What fraction of the original rotational kinetic energy is lost?
Physics
1 answer:
sweet-ann [11.9K]3 years ago
6 0

Answer:

(a)  110 rev/ min

(b) 5/6

Explanation:

As per the conservation of linear momentum,

L ( initial ) = L ( final )

I' ω' = ( I' + I'' ) ωf

I' is the rotational inertia of first wheel and I'' is the rotational inertia of second wheel which is at rest.

(a)

So,    ωf = I' ω' /  ( I' + I'' )

As I'' = 5I'

ωf = I' ω' /  ( I' + 5I' )

ωf = ω'/ 6

now we know ω' = 660 rev /  min

therefore    ωf = 660/6

                       = 110 rev/ min

(b)

Initial kinetic energy will be K'

K' = I'ω'² / 2

and final K.E. will be   K'' =  ( I' + I'' )ωf² / 2

                                   K'' = ( I' + 5I' ) (ω'/ 6)²/ 2

                                   K'' = 6I' ω'²/72

                                   K'' = I' ω'²/ 12

therefore the fraction lost is

                ΔK/K' = ( K' - K'' ) / K'

                           =  {( I'ω'² / 2) - (I' ω'²/ 12)} / ( I'ω'² / 2)

                            = 5/6

You might be interested in
What is the melting point of substance A?
Misha Larkins [42]

Answer:

Solids are easily recognized by their ability to retain a fixed shape and definite volume. Particles making

up a solid are held together in a rigid form. They are not free to move about or slide past one another and

the solid does not have the ability to flow. (Although the particles of a solid do not move position to position, they do have motion in that they are constantly vibrating.

To change the temperature of a solid, heat energy must be added. The amount of heat energy that changes

the temperature of 1.0 g of a solid by 1.0°C is called its specific heat (c). Each substance has its own

specific heat. The specific heat of ice is 2.1 Joules/g°C. In other words we must supply 1.0 gram of ice

with 2.1 Joules of heat energy to raise its temperature by 1.0 °C.

The general equation for calculating heat energy to change the temperature of a solid is:

Heat = Mass x Specific Heat (solid) x Temperature Change

Q = m c DT

10 g 10 g 10 g 10 g 10 g 10 g

Calculate the heat necessary to change 10 g of ice(s) at -20 °C to 10 g of ice(s) at 0°C. (A-B)

Q = mc∆T = (10 g) (2.1 J/g°C) (20°C) = 420 J

If you continue to add heat energy once the temperature of the ice reaches 0°C , the heat absorbed is called

the heat of fusion (Lf). This heat is used to cause a change of phase (from a solid to a liquid). This heat is

increasing the potential energy of the molecules of the solid. No temperature change takes place. Each

substance has its own heat of fusion. The heat of fusion for ice is 340 Joules/g. Exactly the same amount

of heat is given up when 1.0 g of water is changed to ice. This heat is called the heat of crystallization.

The general equation for calculating heat energy to change a solid to a liquid is:

Heat = Mass x Heat of Fusion

Q = m Lf

Calculate the heat necessary to change 10 g of ice(s) at 0°C to 10 g of water(l) at 0°C.(B-C)

Explanation:

Q = mLf = (10 g)( 340 J/g) = 3400 J

3 0
3 years ago
Which of the following does not cause an earthquake
antoniya [11.8K]

Answer:

C

Explanation:

A Tsunami is usually the result of an earthquake under the sea

7 0
3 years ago
Most nuclear waste in the US is ____.
solmaris [256]
The most waste is Yucca mtn. in Nevada
<span />
8 0
3 years ago
Read 2 more answers
Which situation can strengthen a community's stability?
nadya68 [22]
B. Interdependence among specie
7 0
3 years ago
Read 2 more answers
When is a white dwarf formed?
Anna [14]
When a red giant has insufficient mass it pretty much sheds its outer layer to leave the center core know as the white dwarf
6 0
3 years ago
Read 2 more answers
Other questions:
  • What is the kinetic energy of a toy truck with a mass of 0.75 kg and a velocity of 4 m/s? (Formula: )
    10·2 answers
  • Calculate the potential energy of a rock that has a 45 kg mass and is sitting
    6·1 answer
  • A well-thrown ball is caught in a well-padded mitt. If the deceleration of the ball is 2.10×10^{4} 4 m/s^{2} 2 , and 1.85 ms (1
    15·1 answer
  • Two particles A and B start from rest at the origin x = 0 [ft] and move along a straight line such that a = (613) Ift/s) and ag
    8·1 answer
  • A rocket of initial mass 115 kg (including all the contents) has an engine that produces a constant vertical force (the thrust)
    13·1 answer
  • 1000 kg has 50, 000 joules of kinetic energy. what is it's speed?
    15·1 answer
  • The Tevatron acceleator at the Fermi National Accelerator Laboratory (Fermilab) outside Chicago boosts protons to 1 TeV (1000 Ge
    15·1 answer
  • It’s bungee jumping skydiving and hiking
    14·1 answer
  • Which equation shows the relationship of wave speed to
    15·1 answer
  • A vehicle of mass 100kg has a kinetic energy of 5000 J at an instant. The velocity at that instant is​
    7·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!