Answer
Verified
333k+ views
Hint: We are given that the initially wheel starts its rotational motion through rest means initially angular velocity is zero and it reaches 100rev/sec and time taken is 4 sec so we will used equation of angular motion we will find angular acceleration and then we will further proceed with third equation of angular motion to calculate angular displacement.
Formula used:
$\omega '={{\omega }_{{}^\circ }}+\alpha t$
$\theta =\omega t+\dfrac{1}{2}\alpha {{t}^{2}}$
Complete answer:
We are given with following details in the question:
T = time = 4s
Initial angular velocity
${{\omega }_{{}^\circ }}=0$
Final angular velocity
$\omega '=100rev/s$
$\alpha =$Angular acceleration.
We know the formula
$\begin{align}
& \omega '={{\omega }_{{}^\circ }}+\alpha t \\
& 100=0+\alpha \times 4 \\
& \alpha =\dfrac{100}{4} \\
& \alpha =25rev{{s}^{-2}} \\
\end{align}$
Here the angle rotated into three equations of kinematics
We know that
$\begin{align}
& \theta =\omega t+\dfrac{1}{2}\alpha {{t}^{2}} \\
& =0+\dfrac{1}{2}\times 25\times {{4}^{2}} \\
& =8\times 25 \\
& =200\times 2\pi \\
& =400\pi \text{ rad} \\
\end{align}$
Then the angle rotates during these 4 seconds is $400\pi \text{ rad}$.
So, the correct answer is “Option D”.
Additional Information:
There is some ambiguity in what is meant by kinematic expressions for rotational motion. We can also consider the angular displacement and angular velocity as functions of time, given constant angular acceleration, as the kinematic equations. We would consider these to be the result of the application of Newton’s second law for rotational motion about a fixed axis, in the case of constant torque and constant moment of inertia..
Note:
Angular displacement mathematically can be defined as angular velocity times time plus 1/2 angular acceleration times squared. This equation is analogous to the equation for linear displacement.
“Angular displacement can be also known by compounded of angular velocity and angular acceleration”.
The only major problem we face is dealing with torque. In every question of rotation the three things that we must know is how to deal with torque during rotational motion, rotational + translational motion and equilibrium condition
Formula used:
$\omega '={{\omega }_{{}^\circ }}+\alpha t$
$\theta =\omega t+\dfrac{1}{2}\alpha {{t}^{2}}$
Complete answer:
We are given with following details in the question:
T = time = 4s
Initial angular velocity
${{\omega }_{{}^\circ }}=0$
Final angular velocity
$\omega '=100rev/s$
$\alpha =$Angular acceleration.
We know the formula
$\begin{align}
& \omega '={{\omega }_{{}^\circ }}+\alpha t \\
& 100=0+\alpha \times 4 \\
& \alpha =\dfrac{100}{4} \\
& \alpha =25rev{{s}^{-2}} \\
\end{align}$
Here the angle rotated into three equations of kinematics
We know that
$\begin{align}
& \theta =\omega t+\dfrac{1}{2}\alpha {{t}^{2}} \\
& =0+\dfrac{1}{2}\times 25\times {{4}^{2}} \\
& =8\times 25 \\
& =200\times 2\pi \\
& =400\pi \text{ rad} \\
\end{align}$
Then the angle rotates during these 4 seconds is $400\pi \text{ rad}$.
So, the correct answer is “Option D”.
Additional Information:
There is some ambiguity in what is meant by kinematic expressions for rotational motion. We can also consider the angular displacement and angular velocity as functions of time, given constant angular acceleration, as the kinematic equations. We would consider these to be the result of the application of Newton’s second law for rotational motion about a fixed axis, in the case of constant torque and constant moment of inertia..
Note:
Angular displacement mathematically can be defined as angular velocity times time plus 1/2 angular acceleration times squared. This equation is analogous to the equation for linear displacement.
“Angular displacement can be also known by compounded of angular velocity and angular acceleration”.
The only major problem we face is dealing with torque. In every question of rotation the three things that we must know is how to deal with torque during rotational motion, rotational + translational motion and equilibrium condition
Recently Updated Pages
Assertion The resistivity of a semiconductor increases class 13 physics CBSE
The branch of science which deals with nature and natural class 10 physics CBSE
What is the stopping potential when the metal with class 12 physics JEE_Main
The momentum of a photon is 2 times 10 16gm cmsec Its class 12 physics JEE_Main
How do you arrange NH4 + BF3 H2O C2H2 in increasing class 11 chemistry CBSE
Is H mCT and q mCT the same thing If so which is more class 11 chemistry CBSE
Trending doubts
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
Write an application to the principal requesting five class 10 english CBSE
Difference Between Plant Cell and Animal Cell
a Tabulate the differences in the characteristics of class 12 chemistry CBSE
Change the following sentences into negative and interrogative class 10 english CBSE
What organs are located on the left side of your body class 11 biology CBSE
Discuss what these phrases mean to you A a yellow wood class 9 english CBSE
List some examples of Rabi and Kharif crops class 8 biology CBSE