- #1
blue5t1053
- 23
- 1
Problem:
A disk rotates about its central axis starting from rest and accelerates with constant angular acceleration. At one time it is rotating at 12 rev/s; 69 revolutions later, its angular speed is 33 rev/s. Calculate (a) the angular acceleration, (b) the time required to complete the 69 revolutions, (c) the time required to reach the 12 rev/s angular speed, and (d) the number of revolutions from rest until the time the disk reaches 12 rev/s angular speed.
My work:
part (a): <br /> \omega ^{2} = \omega ^{2}_{0} + 2 \alpha (\vartheta - \vartheta _{0}) \Rightarrow \frac{2 * \pi * (33^{2} rev/s - 12^{2} rev/s)}{2 * 69 sec} = 43.03 rad/s^{2}
part (b): <br /> \vartheta =\vartheta \frac{1}{2} (\omega _{0} + \omega)* t \Rightarrow \frac{2 * 69 sec}{12 rev/s + 33 rev/s} = 3.07 sec
part (c): <br /> \omega ^{2} = \omega ^{2}_{0} + 2 \alpha (\vartheta - \vartheta _{0}) \Rightarrow \frac{(33^{2} rev/s - 12^{2} rev/s)}{2 * 69 sec} = 6.85 rev/s^{2};
\omega = \omega _{0} + \alpha * t \Rightarrow \frac{12 rev/s}{6.85 rev/s^{2}} = 1.75 sec
part (d): <br /> \omega ^{2} = \omega ^{2}_{0} + 2 \alpha (\vartheta - \vartheta _{0}) \Rightarrow \frac{(12^{2} rev/s - 0^{2} rev/s)}{2 * 6.85 rev/s^{2}} = 10.5 rev
I think I did it correctly, but I would appreciate if I could have my work checked since it's the first time I've done angular acceleration. Thank you.
A disk rotates about its central axis starting from rest and accelerates with constant angular acceleration. At one time it is rotating at 12 rev/s; 69 revolutions later, its angular speed is 33 rev/s. Calculate (a) the angular acceleration, (b) the time required to complete the 69 revolutions, (c) the time required to reach the 12 rev/s angular speed, and (d) the number of revolutions from rest until the time the disk reaches 12 rev/s angular speed.
My work:
part (a): <br /> \omega ^{2} = \omega ^{2}_{0} + 2 \alpha (\vartheta - \vartheta _{0}) \Rightarrow \frac{2 * \pi * (33^{2} rev/s - 12^{2} rev/s)}{2 * 69 sec} = 43.03 rad/s^{2}
part (b): <br /> \vartheta =\vartheta \frac{1}{2} (\omega _{0} + \omega)* t \Rightarrow \frac{2 * 69 sec}{12 rev/s + 33 rev/s} = 3.07 sec
part (c): <br /> \omega ^{2} = \omega ^{2}_{0} + 2 \alpha (\vartheta - \vartheta _{0}) \Rightarrow \frac{(33^{2} rev/s - 12^{2} rev/s)}{2 * 69 sec} = 6.85 rev/s^{2};
\omega = \omega _{0} + \alpha * t \Rightarrow \frac{12 rev/s}{6.85 rev/s^{2}} = 1.75 sec
part (d): <br /> \omega ^{2} = \omega ^{2}_{0} + 2 \alpha (\vartheta - \vartheta _{0}) \Rightarrow \frac{(12^{2} rev/s - 0^{2} rev/s)}{2 * 6.85 rev/s^{2}} = 10.5 rev
I think I did it correctly, but I would appreciate if I could have my work checked since it's the first time I've done angular acceleration. Thank you.