A body has translatory motion if it moves along a

A Ferris wheel starts at rest and builds up to a final angular speed of 0.70 rad/s while rotating through an angular displacemen

PilotLPTM [1.2K]

Answer:

The average angular acceleration is 0.05 radians per square second.

Explanation:

Let suppose that Ferris wheel accelerates at constant rate, the angular acceleration as a function of change in angular position and the squared final and initial angular velocities can be clear from the following expression:

$\omega^{2} = \omega_{o}^{2} + 2 \cdot \alpha\cdot (\theta-\theta_{o})$

Where:

$\omega_{o}$ , $\omega$ - Initial and final angular velocities, measured in radians per second.

$\alpha$ - Angular acceleration, measured in radians per square second.

$\theta_{o}$ , $\theta$ - Initial and final angular position, measured in radians.

Then,

$\alpha = \frac{\omega^{2}-\omega_{o}^{2}}{2\cdot (\theta-\theta_{o})}$

Given that $\omega_{o} = 0\,\frac{rad}{s}$ , $\omega = 0.70\,\frac{rad}{s}$ and $\theta-\theta_{o} = 4.9\,rad$ , the angular acceleration is:

$\alpha = \frac{\left(0.70\,\frac{rad}{s} \right)^{2}-\left(0\,\frac{rad}{s} \right)^{2}}{2\cdot \left(4.9\,rad\right)}$

$\alpha = 0.05\,\frac{rad}{s^{2}}$

Now, the time needed to accelerate the Ferris wheel uniformly is described by this kinematic equation:

$\omega = \omega_{o} + \alpha \cdot t$

Where $t$ is the time measured in seconds.

The time is cleared and obtain after replacing every value:

$t = \frac{\omega-\omega_{o}}{\alpha}$

If $\omega_{o} = 0\,\frac{rad}{s}$ , $\omega = 0.70\,\frac{rad}{s}$ and $\alpha = 0.05\,\frac{rad}{s^{2}}$ , the required time is:

$t = \frac{0.70\,\frac{rad}{s} - 0\,\frac{rad}{s} }{0.05\,\frac{rad}{s^{2}} }$

$t = 14\,s$

Average angular acceleration is obtained by dividing the difference between final and initial angular velocities by the time found in the previous step. That is:

$\bar \alpha = \frac{\omega-\omega_{o}}{t}$

If $\omega_{o} = 0\,\frac{rad}{s}$ , $\omega = 0.70\,\frac{rad}{s}$ and $t = 14\,s$ , the average angular acceleration is:

$\bar \alpha = \frac{0.70\,\frac{rad}{s} - 0\,\frac{rad}{s} }{14\,s}$

$\bar \alpha = 0.05\,\frac{rad}{s^{2}}$

The average angular acceleration is 0.05 radians per square second.

4 0

2 years ago

The difference between the Carbon 12 and Carbon 14 isotopes is the

Elina [12.6K]

Answer:
The number of neutrons.

Explaination:
The atoms of carbon 12 contain 6 neutrons while the atoms of carbon 14 contain 8 neutrons

4 0

2 years ago

A plumber is going to put two pipes in a wall, one in front and one in back. The pipes will be touching once they are installed.

beks73 [17]

Answer:

They become the same exact tempature

Explanation:

Since they got connected it should be the same.

8 0

2 years ago

The kinetic energy of a book on a shelf is equal to the work done to lift the book to the shelf. t/f

Svet_ta [14]

The kinetic energy of a book on a shelf is equal to the work done to lift the book to the shelf is false. The kinetic energy on the shelf is zero because it is not in action.

7 0

3 years ago

Read 2 more answers

The Doppler shift can be observed when ____________. Check all that apply. Group of answer choices the source of sound moves tow

castortr0y [4]

Answer:

the source of sound moves towards an observe

Explanation:

The Doppler effect is related to waves such as sound or light. the effect causes an increase or decrease in the frequency of sound light or other waves when the souces either move towards or away from the observer. For example the siren of the train to a person on the platform, the redshift seen by astronomers.

Therefore, The Doppler shift can be observed when the source of sound moves towards an observer From a place closer to the observer than the last wave's crest, each consecutive wave crest is sent. Each wave therefore, takes a little less time than the preceding wave to reach the observer.

6 0

2 years ago