Westonci.ca offers quick and accurate answers to your questions. Join our community and get the insights you need today. Explore comprehensive solutions to your questions from knowledgeable professionals across various fields 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].
Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. Thank you for trusting Westonci.ca. Don't forget to revisit us for more accurate and insightful answers.
