A heavy flywheel is accelerated (rotationally) by a motor thatprovides constant torque and therefore a constant angula…
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Question “A heavy flywheel is accelerated (rotationally) by a motor thatprovides constant torque and therefore a constant angula…”
thatprovides constant torque and therefore a constant
angularacceleration . The
flywheel is assumed to be at rest at time in
Parts A and B of this problem.
which the flywheel will have turned during thetime it takes for it
to accelerate from rest up to angular velocity.
which the flywheel will have turned during thetime it takes for it
to accelerate from rest up to angular velocity.
thewheel up to an angular velocity with
angular acceleration in
time . At this
point, the motor is turned off and a brake isapplied that
decelerates the wheel with a constant angularacceleration of
.
Find , the time
it will take the wheel to stop after the brakeis applied (that is,
the time for the wheel to reach zero angularvelocity).
Answer
Rotational kinematics equations are the main idea that solves this problem.
To calculate the flywheel’s time to achieve angular acceleration, first use the constant angle equation for rotational kinematics. To calculate the angle through the flywheel during the time interval, later use the constant angular equation to calculate angular displacement. To find the stop time, you can use the constant angle equation for rotational kinematics.
This is how the constant angular acceleration equation can be expressed:
{\omega _1} = {\omega _0} + \alpha tHere, {\omega _1}
This equation combines the constant angular acceleration and the angular displacement.
\theta = {\omega _0}t + \frac{1}{2}\alpha {t^2}Here, \theta
(a)
Calculate how long it takes for the flywheel to achieve an angular acceleration.
This is how the constant angular acceleration equation can be expressed:
{\omega _1} = {\omega _0} + \alpha tHere, {\omega _1}
Substitute 0 for $math_tag_6
\begin{array}{c}\\{\omega _1} = \left( 0 \right) + \alpha {t_1}\\\\{t_1} = \frac{{{\omega _1}}}{\alpha }\\\end{array}(b)
Calculate the angle displacement.
This equation combines the constant angular acceleration and the angular displacement.
\theta = {\omega _0}t + \frac{1}{2}\alpha {t^2}Here, \theta
Substitute $math_tag_6 for 0
\begin{array}{c}\\{\theta _1} = \left( {0\,{\rm{rad/s}}} \right){t_1} + \frac{1}{2}\alpha {t_1}^2\\\\{\theta _1} = \frac{1}{2}\alpha {t_1}^2\\\end{array}(c)
Calculate how long it takes for the flywheel to stop following the application of brakes.
This is how the constant angular acceleration equation can be expressed:
{\omega _1} = {\omega _0} + \alpha tHere, {\omega _1}
The angular velocity $math_tag_6 was at its highest point just before the motor was turned off.
The initial conditions are now different. In this instance, wheel is spinning initially and angular acceleration differs.
Substitute $math_tag_6 for 0
\begin{array}{c}\\\left( 0 \right) = {\omega _1} + \left( { - 5\alpha } \right){t_2}\\\\{t_2} = \frac{{{\omega _1}}}{{5\alpha }}\\\end{array}Ans Part a
The flywheel takes $math_tag_17 to achieve angular acceleration
Conclusion
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