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
sergiy2304 [10]
2 years ago
7

A wheel has a radius of r = 2.0 m and it rolls down a smooth incline. The height of the incline is h = 8.0 m . What is the angul

ar velocity ω of the wheel at the bottom of the incline?
Express your answer in radians per second.
Physics
2 answers:
Zolol [24]2 years ago
7 0

The angular velocity of the wheel depends on the mass, radius and the

mode of rotation of the wheel (with or without slipping).

  • The angle velocity at the bottom of the incline, ω ≈ <u>4.43 rad/sec</u>

Reasons:

The given parameters are;

Radius of the wheel, r = 2.0 m

Height of the incline, h = 8.0 m

Required:

Angular velocity of the wheel at the bottom of the incline.

Solution:

The potential energy of the wheel at the top of the hill, P.E. = m·g·h

Sum \ of \  the \  kinetic  \ energy  \ of  \ the \  wheel,  \ K.E. = \mathbf{\displaystyle \frac{1}{2} \cdot m \cdot v^2 + \frac{1}{2} \cdot I \cdot \omega ^2}

Where;

v = The translational velocity of the wheel = ω·r

I = The moment of inertia of the wheel = m·r²

Therefore'

Sum \ of \   K.E. = \displaystyle \frac{1}{2} \cdot m \cdot (\omega \cdot r)^2 + \frac{1}{2} \cdot m \cdot r^2 \cdot \omega ^2 =  \mathbf{m \cdot r^2 \cdot  \omega^2}

At the bottom of the hill, the potential energy is converted to kinetic energy

Therefore;

P.E. = Sum of K.E.

m·g·h = m·r²·ω²

g·h = r²·ω²

\displaystyle \omega = \sqrt{ \frac{g \cdot h}{r^2} } = \mathbf{ \frac{\sqrt{g \cdot h} }{r}}

Where;

g = Acceleration due to gravity ≈ 9.81 m/s²

Therefore;

\displaystyle \omega = \frac{\sqrt{9.81 \times 8} }{2} \approx \mathbf{ 4.43}

  • The angular velocity of the of the wheel at the bottom of the incline, ω ≈ 4.43 rad/sec

Learn more about the law of conservation of energy here:

brainly.com/question/4723473

brainly.com/question/2292427

brainly.com/question/816294

zepelin [54]2 years ago
4 0

The angular velocity of the wheel at the bottom of the incline is 4.429 rad/sec

The angular velocity (ω) of an object is the rate at which the object's angle position is changing in relation to time.

For a wheel attached to an incline angle, the angular velocity can be computed by considering the conservation of energy theorem.

As such the total kinetic energy (K.E) and rotational kinetic energy (R.K.E) at a point is equal to the total potential energy (P.E) at the other point.

i.e.

P.E = K.E + R.K.E

\mathbf{mgh = \dfrac{1}{2}m(r \times \omega)^2 + \dfrac{1}{2}\times I \times \omega^2}

\mathbf{gh = \dfrac{1}{2}(r \times \omega)^2 + \dfrac{1}{2}\times r^2 \times \omega^2}

\mathbf{2 \times \dfrac{gh}{r^2} =\omega^2 +  \omega^2}

\mathbf{2 \omega^2=2 \times \dfrac{9.81 \times 8 m }{2.0 ^2}  }

\mathbf{\omega^2=\dfrac{39.24 }{2}}

\mathbf{\omega=\sqrt{19.62 } \ rad/sec}

\mathbf{\omega=4.429 \ rad/sec}

Therefore, we can conclude that the angular velocity of the wheel at the bottom of the incline is 4.429 rad/sec

Learn more about angular velocity here:

brainly.com/question/1452612

You might be interested in
Two resistors, A and B, are connected in series to a 6.0 V battery. A voltmeter connected across resistor A measures a potential
mestny [16]

Answer:

Resistance of resistor A = 6.0 Ω and resistance of resistor B = 3.0 Ω

Explanation:

When the two resistors are in series, let V₁ = voltage in resistor A and R₁ = resistance of resistor A and V₂ = voltage in resistor B and R₂ = resistance of resistor B.

Given that V₁ + V₂ = 6.0 V and V₁ = 4.0 V,

V₂ = 6.0 V - V₁ = 6.0 V - 4.0 V = 2.0 V

Also, let the current in series be I.

So, V₁ = IR₁ and V₂ = IR₂

I = V₁/R₁ and I = V₂/R₂

equating both expressions, we have

V₁/R₁ = V₂/R₂

4.0 V/R₁ = 2.0 V/R₂

dividing through by 2.0 V, we have

2/R₁ = 1/R₂

taking the reciprocal, we have

R₂ = R₁/2

R₁ = 2R₂

From the parallel connection, let V₁ = voltage in resistor A and R₁ = resistance of resistor A and V₂ = voltage in resistor B and R₂ = resistance of resistor B. Since it is parallel, V₁ = V₂ = V = 6.0 V

Also, V₂ = I₂R₂ where I₂ = current in resistor B = 2.0 A and R₂ = resistance of resistor B

So, R₂ = V₂/I₂

= 6.0 V/2.0 A

= 3.0 Ω

R₁ = 2R₂

= 2(3.0 Ω)

= 6.0 Ω

So, resistance of resistor A = 6.0 Ω and resistance of resistor B = 3.0 Ω

6 0
3 years ago
Which things determine an element's electronegativity? Check all that apply. A. The size of the atom of that element B. Whether
KengaRu [80]
D. The number of electrons
6 0
3 years ago
When a wire moves through a magnetic field, an electric current is produced in the wire. Why does this phenomenon occur?
Alenkasestr [34]

Answer:

<h2>It occurs whenever a magnetic field and an electric conductor move relative to one another so the conductor crosses lines of force in the magnetic field. </h2>

Explanation:

<h3>The current produced by electromagnetic induction is greater when the magnet or coil moves faster, the coil has more turns, or the magnet is stronger.</h3>

<h2>Carryonlearning </h2>
4 0
2 years ago
A laser beam is incident at an angle of 33.0° to the vertical onto a solution of cornsyrup in water.(a) If the beam is refracted
IrinaK [193]

Answer:

1.29649

488.08706 nm

6.14644\times 10^{14}\ Hz

231715700.28346 m/s

Explanation:

n denotes refractive index

1 denotes air

2 denotes solution

\lambda_0 = 632.8 nm

From Snell's law we have the relation

n_1sin\theta_1=n_2sin\theta_2\\\Rightarrow n_2=\dfrac{n_1sin\theta_1}{sin\theta_2}\\\Rightarrow n_2=\dfrac{1\times sin33}{sin24.84}\\\Rightarrow n_2=1.29649

Refractive index of the solution is 1.29649

Wavelength is given by

\lambda=\dfrac{\lambda_0}{n_2}\\\Rightarrow \lambda=\dfrac{632.8}{1.29649}\\\Rightarrow \lambda=488.08706\ nm

The wavelength of the solution is 488.08706 nm

Frequency is given by

f=\dfrac{c}{\lambda}\\\Rightarrow f=\dfrac{3\times 10^8}{488.08706\times 10^{-9}}\\\Rightarrow f=6.14644\times 10^{14}\ Hz

The frequency is 6.14644\times 10^{14}\ Hz

v=\dfrac{c}{n_2}\\\Rightarrow v=\dfrac{3\times 10^8}{1.29469}\\\Rightarrow v=231715700.28346\ m/s

The speed in the solution is 231715700.28346 m/s

8 0
3 years ago
The circumference of a bicycle wheel is 2 meters. if it rotates at 1 revolution per second then its linear speed is
tester [92]
Given:
Circumference = 2 m
Angular speed,  ω = 1 rev/s = 2π radians/s

If the radius is r, then
2πr = 2 
r = 1/π m

The linear (tangential) speed is
v = rω
   = (1/π m)*(2π rad/s) = 0.5 m/s

Answer: 0.5 m/s
6 0
3 years ago
Other questions:
  • A typical loaded commercial jet airplane has an inertia of 2.1 × 105 kg (a) Which do you expect to require more energy: getting
    9·1 answer
  • Which of the following is an example of transmission of light? A. Light passes through a glass of water. B. A visor blocks sunli
    5·2 answers
  • Calculate the total resistance in a parallel circuit made up of resistances of 2, 3, and 4.
    12·1 answer
  • Oil flows upward in the wick of a lantern because of the liquid property called
    7·1 answer
  • Please Help!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
    12·1 answer
  • Two technicians are discussing disc brake rotor service. Technician A says that the inner races (bearing cups) should be removed
    15·1 answer
  • Can someone tell me the answers??? thanks i need it asap!! i will give brainlist!!
    6·2 answers
  • 100 Pascal is equal to:<br> A) 100 Newton B) 1000N/m2 C) 100N/m2 D) 10,000N/m2 E) None of these
    12·2 answers
  • How are traits influenced by the environment? (No links)
    15·1 answer
  • An astronaut weighs 200 N on the Moon where gravity is 1.62 m/s/s. Find his weight on Earth. HELP PLEASE FAST
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!