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
Alexeev081 [22]
3 years ago
7

Calculate the moment of inertia and the rotational kinetic energy for the following objects spinning about a central axis (in un

its of Joules): a solid sphere with a mass of 200 grams and a radius of 5.0 cm rotating with an angular speed of 2.5 rad/sec. a thin spherical shell with a mass of 200 grams and a radius of 5.0 cm rotating with an angular speed of 2.5 rad/sec. a solid cylinder with a mass of 200 grams and a radius of 5.0 cm rotating with an angular speed of 2.5 rad/sec. a hoop with a mass of 200 grams and a radius of 5.0 cm rotating with an angular speed of 2.5 rad/sec.
Physics
1 answer:
Helga [31]3 years ago
6 0

Answer:

a) K = 6.25 10⁻⁴ J , b)  K = 10.41  10⁻⁴ J , c)  K = 7.81 10⁻⁴ J , d)  K = 15.625 10⁻⁴ J

Explanation:

The moment of inertia is

         I = ∫ r² dm

For high symmetry bodies it is tabulated.

The rotational kinetic energy is

         K = ½ I w²

Let's calculate the values ​​of the given bodies

a) solid sphere

         I = 2/5 M R²

         I = 2/5 0.200 0.05²

         I = 2 10⁻⁴ kg m²

        K = ½ 2 10⁻⁴ 2.5²

        K = 6.25 10⁻⁴ J

b) spherical shell

        I = 2/3 M R²

        I = 2/3 0.200 0.05²

        I = 3.33 10⁻⁴ kg m²

        K = ½ 3.33 10-4 2.5²

        K = 10.41  10⁻⁴ J

c) solid cylinder

        I = ½ M R²

        I = ½ 0.200 0.05²

        I = 2.5 10⁻⁴ kg m²

       K = ½ 2.5 10-4 2.5²

       K = 7.81 10⁻⁴ J

d) hoop

       I = M R²

       I = 0.200 0.05²

       I = 5 10⁻⁴ kg m²

      K = ½ 5 10⁻⁴ 2.5²

      K = 15.625 10⁻⁴ J

You might be interested in
A 40-cmcm-long tube has a 40-cmcm-long insert that can be pulled in and out. A vibrating tuning fork is held next to the tube. A
Licemer1 [7]

Answer:

1070 Hz

Explanation:

First, I should point out there might be a typo in the question or the question has inconsistent values. If the tube is 40 cm long, standing waves cannot be produced at 42.5 cm and 58.5 cm lengths. I assume the length is more than the value in the question then. Under this assumption, we proceed as below:

The insert in the tube creates a closed pipe with one end open and the other closed. For a closed pipe, the difference between successive resonances is a half wavelength \frac{\lambda}{2}.

Hence, we have

\dfrac{\lambda}{2}=58.5-42.5=16 \text{ cm}

\lambda=32\text{ cm}=0.32 \text{ m}.

The speed of a wave is the product of its wavelength and its frequency.

v=f\lambda

f=\dfrac{v}{\lambda}

f=\dfrac{343}{0.32}=1070 \text{ Hz}

7 0
3 years ago
José and Laurel measured the length of a stick's shadow during the day. Without knowing the length of the stick, which of their
skelet666 [1.2K]

Answer:

Option B.

Explanation:

Assuming the stick is in vertical position, its shadow depends on two factors: its length and the angle between the sun rays and the stick. When the angle is bigger, the lenght of the shadow increases, and vice versa. So, when the sun rays are parallel to the stick, the shadow may be small. Since they are nearly perpendicular to the Earth's surface at 12 o'clock, the shadow of the stick at that time should be minimal. It means that the measured shadow of 75 cm at 12:30 p.m. is almost impossible (Option B).

5 0
2 years ago
20 POINTSSS!!!!!!!!
Soloha48 [4]
Answer: A
Hope this help you!!
7 0
3 years ago
Waves in a fish bowl jostled by the Thingamajigger move to the sides at an average velocity of 0.50 m/s. If they occur once ever
Colt1911 [192]

Answer:

0.125 m

Explanation:

In this problem, we have:

v = 0.50 m/s is the average velocity of the wave

T = 0.25 s is the period of the wave

We can find the frequency of the wave, which is equal to the reciprocal of the period:

f=\frac{1}{T}=\frac{1}{0.25 s}=4 Hz

The problem is asking us to find the distance between two crests of the wave: this is equivalent to the wavelength. The wavelength is related to the average velocity and the frequency by the formula:

\lambda=\frac{v}{f}

Substituting the numerical values, we find

\lambda=\frac{0.5 m/s}{4 Hz}=0.125 m

4 0
3 years ago
A rope of length L has circular cross-sectional area A and density rho = m/V , where m is the mass of the rope and V = A · L is
hram777 [196]

Answer: µ = ρ¹ * A¹

Where x=1 and y=1

Explanation: According to the question, the mass per unit length (µ) is related to the density (ρ) and area A are related by the formulae below

µ = ρ * A

The dimension for each of these quantities is given below

Since µ is mass per unit length, unit is Kg/m and the dimension is ML^-1

ρ is density with unit kg/m³ and the dimension is ML^3

A is area with unit m², thus the dimension is M^2

Note that using dimensional analysis means we will be using the 3 fundamental quantities (mass, length and time) in our analysis.

Their dimensions below

Mass = M

Length = L

Time = T

Since the mass per unit length is related to density and area, we have a mathematical equation to provide a solution as shown below

µ = ρ^x * A^y.

By getting the power of x and y we will be able to get the formula that relates the quantities.

This is done by slotting in the dimensions of the respective quantities.

ML^-1 = (ML^-3)^x * (L²) ^y

By using law of indices on the right hand side of the equation, we have that

ML^-1 = (M^x * L^-3x) * (L^2y)

Also applying law of indices on the right hand side, we have that

ML^-1 = (M^x) * (L^-3x +2y)

The next step is to relate equal variables on both sides

For the M variable

M¹ = M^x which results to

x = 1

For the L variable

L^-1 = L^-3x+2y which results to

-1 = - 3x +2y

But x = 1

We have that

-1 = - 3(1) +2y

-1 = - 3 + 2y

-1 +3= 2y

2 = 2y

y = 1

Thus x=1 and y=1 and the formulae that relates the quantities is

µ = ρ¹ * A¹

3 0
2 years ago
Other questions:
  • Which statement best describes the difference between acceleration and deceleration?
    13·1 answer
  • What type of motion occurs when an object spins around an axis without altering its linear position?
    12·1 answer
  • Why are the spheres representing nitrogen and oxygen different colors
    8·1 answer
  • spring stretches by 21.0 cm when a 135 N object is attached. What is the weight of a fish that would stretch the spring by 43.9
    6·1 answer
  • The FIRST space station placed into orbit around the earth followed by a team sent from earth to link up with the station was de
    6·2 answers
  • A radar antenna is tracking a satellite orbiting the earth. At a certain time, the radar screen shows the satellite to be 118 km
    9·1 answer
  • An astronaut is taking a space walk near the shuttle when her safety tether breaks. what should the astronaut do to get back to
    10·1 answer
  • A book rests on a table, exerting a downward force on the table. the reaction to this force is:
    11·1 answer
  • A car traveling at point k the car travels south for 8.0 km it then travels west for 5.0 km next it travels for 4,0 what is the
    14·1 answer
  • 11 cm/s2 is an example of<br> 30 m/s northwest is an example of
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!