Looking for reliable answers? Westonci.ca is the ultimate Q&A platform where experts share their knowledge on various topics. Get immediate and reliable solutions to your questions from a community of experienced professionals on our platform. Join our Q&A platform to connect with experts dedicated to providing accurate answers to your questions in various fields.
Sagot :
Answer:
A. 0.502
B. 0.753
Explanation:
A. The angular acceleration of the flywheel is equal to the change in angular velocity divided by the change in time, which is equal to (4.6-2.09)/5 which is 0.502.
B. Angular acceleration is equal to the net torque divided by the rotational inertia. If you rearrange the equation, torque is equal to angular acceleration times rotational inertia, which is 0.502 times 1.5 which is 0.753.
Answer:
Assumption: the angular acceleration of this flywheel is constant.
Angular acceleration: [tex]0.502\; {\rm rad\cdot s^{-2}}[/tex].
Net torque on this flywheel: [tex]0.753\; {\rm kg \cdot m^{2} \cdot s^{-2}[/tex] (or, equivalently, [tex]0.753\; {\rm N \cdot m}[/tex].)
Explanation:
Change in the angular velocity of this flywheel:
[tex]\begin{aligned}\Delta \omega &= \omega_{1} - \omega_{0} \\ &= 4.6\; {\rm rad \cdot s^{-1}} - 2.09 \; {\rm rad \cdot s^{-1}} \\ &= 2.51\; {\rm rad \cdot s^{-1}}\end{aligned}[/tex].
Divide this change in angular velocity [tex]\Delta \omega[/tex] with the duration [tex]t[/tex] of the acceleration to find the average angular acceleration of this flywheel:
[tex]\begin{aligned}\alpha &= \frac{\Delta \omega}{t} \\ &= \frac{2.51\; {\rm rad \cdot s^{-1}}}{5\; {\rm s}} \\ &= 0.502\; {\rm rad \cdot s^{-2}}\end{aligned}[/tex].
By Newton's Second Law for Rotation, the net torque on this flywheel would be the product of the angular acceleration and the moment of inertia of this flywheel, [tex]I[/tex]:
[tex]\begin{aligned}\tau_{\text{net}} &= I\, \alpha \\ &= 1.5\; {\rm kg \cdot m^{2}} \times 0.502\; {\rm s^{-2}} \\ &= 0.753\; {\rm kg \cdot m^{2} \cdot s^{-2}} \\ &= 0.753\; {\rm (kg \cdot m \cdot s^{-2}) \cdot m} \\ &= 0.753\; {\rm N \cdot m}\end{aligned}[/tex].
We appreciate your visit. Hopefully, the answers you found were beneficial. Don't hesitate to come back for more information. Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. Thank you for visiting Westonci.ca, your go-to source for reliable answers. Come back soon for more expert insights.
