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
Zielflug [23.3K]
3 years ago
10

Starting from rest, a disk rotates about its central axis with constant angular acceleration. In 1.00 s, it rotates 21.0 rad. Du

ring that time, what are the magnitudes of (a) the angular acceleration and (b) the average angular velocity? (c) What is the instantaneous angular velocity of the disk at the end of the 1.00 s? (d) With the angular acceleration unchanged, through what additional angle (rad) will the disk turn during the next 1.00 s?
Physics
1 answer:
ELEN [110]3 years ago
5 0

With constant angular acceleration \alpha, the disk achieves an angular velocity \omega at time t according to

\omega=\alpha t

and angular displacement \theta according to

\theta=\dfrac12\alpha t^2

a. So after 1.00 s, having rotated 21.0 rad, it must have undergone an acceleration of

21.0\,\mathrm{rad}=\dfrac12\alpha(1.00\,\mathrm s)^2\implies\alpha=42.0\dfrac{\rm rad}{\mathrm s^2}

b. Under constant acceleration, the average angular velocity is equivalent to

\omega_{\rm avg}=\dfrac{\omega_f+\omega_i}2

where \omega_f and \omega_i are the final and initial angular velocities, respectively. Then

\omega_{\rm avg}=\dfrac{\left(42.0\frac{\rm rad}{\mathrm s^2}\right)(1.00\,\mathrm s)}2=42.0\dfrac{\rm rad}{\rm s}

c. After 1.00 s, the disk has instantaneous angular velocity

\omega=\left(42.0\dfrac{\rm rad}{\mathrm s^2}\right)(1.00\,\mathrm s)=42.0\dfrac{\rm rad}{\rm s}

d. During the next 1.00 s, the disk will start moving with the angular velocity \omega_0 equal to the one found in part (c). Ignoring the 21.0 rad it had rotated in the first 1.00 s interval, the disk will rotate by angle \theta according to

\theta=\omega_0t+\dfrac12\alpha t^2

which would be equal to

\theta=\left(42.0\dfrac{\rm rad}{\rm s}\right)(1.00\,\mathrm s)+\dfrac12\left(42.0\dfrac{\rm rad}{\mathrm s^2}\right)(1.00\,\mathrm s)^2=63.0\,\mathrm{rad}

You might be interested in
A force is a vector quantity. What does that mean?
Inga [223]

Answer: Acceleration due to gravity

Explanation: Force, F = mg, is a vector quantity because the acceleration due to gravity, g, is a vector quantity. Explanation: F = mg Where m is the mass (in kilograms) of the object in question and g is the acceleration due to gravity. Mass is a scalar quantity; mass has no dependence on direction whatsoever.

5 0
2 years ago
A pickup truck is being driven down the highway carrying eight 100 gallon fish tank full of water. A hole is punctured in each t
irakobra [83]

Answer:

Explanation:

The velocity of the vehicle would increase because the the tanks (when filled with water) must have exerted a force which would reduce the velocity of the vehicle at a certain pressure on the gas pedal. Note that force equals mass multiplied by acceleration; as the mass decreases, so the force decreases. Thus, when the mass exerted by this tanks (on the vehicle) decrease as a result of the hole punctured in them, the force exerted by the tanks would also decrease causing an increase in velocity of the pick up truck when the same pressure is applied on the gas pedal throughout (before and after the puncture).

The conservation law that applied here is the law of conservation of energy which states that energy can neither be created nor destroyed but can be transformed from one form to another. This is because the energy the vehicle used in carrying the load (the tanks) was transformed to the energy that resulted in increasing  it's velocity (no new energy was formed as the pressure on the gas pedal remained the same).

6 0
3 years ago
In longitudinal waves the places where the coils are bunched together are called *
Firdavs [7]
In longitudinal waves the places where the coils are bunched together are called *
Compressions
3 0
3 years ago
Approximately what percentage of the calories you take in every day are consumed by your brain's activity?
777dan777 [17]
It consumes about 20%
3 0
3 years ago
One gram of salt in 100 liters of water could be considered a _______________________ solution
Doss [256]
That would be a diluted solution

5 0
3 years ago
Read 2 more answers
Other questions:
  • Ted Clubber Lang. A hook in boxing primarily involves horizontal flexion of the shoulder while maintaining a constant angle at t
    9·1 answer
  • In the 2008 Olympics, Jamaican sprinter Usain Bolt shocked the world as he ran the 100-meter dash in 9.69 seconds. Determine Usa
    10·1 answer
  • A 92-kg astronaut and a 2000-kg satellite are at rest relative to a space station. the astronaut pushes on the satellite, giving
    9·2 answers
  • HELP ME
    12·1 answer
  • Prove the three laws of motion​
    15·2 answers
  • When the C4 key on a piano keyboard is pressed, a string inside the piano is struck by a hammer and begins vibrating back and fo
    6·1 answer
  • A solenoid of length 0.35 m and diameter 0.040 m carries a current of 5.0 A through its windings. If the magnetic field in the c
    12·1 answer
  • A fisherman moves from one end of a boat to another
    11·1 answer
  • What is the 5 quantitative research problems?<br>​
    12·1 answer
  • What is TRUE of carbon monoxide?
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!