Westonci.ca is your go-to source for answers, with a community ready to provide accurate and timely information. Experience the convenience of getting accurate answers to your questions from a dedicated community of professionals. Explore comprehensive solutions to your questions from knowledgeable professionals across various fields on our platform.
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. We're here to help at Westonci.ca. Keep visiting for the best answers to your questions.