P=change in E/t
Change in E=p*t
=15*3
=45
The answer is 45J.
A drummer would loosen the drum skin in order to make the sound of a drum give a note of lower pitch.
However, I am not entirely sure.
Answer:
Rod 1 has greater initial angular acceleration; The initial angular acceleration for rod 1 is greater than for rod 2.
Explanation:
For the rod 1 the angular acceleration is
Similarly, for rod 2
![\alpha_2 = \dfrac{\tau_2}{I_2}.](https://tex.z-dn.net/?f=%5Calpha_2%20%3D%20%5Cdfrac%7B%5Ctau_2%7D%7BI_2%7D.)
Now, the moment of inertia for rod 1 is
,
and the torque acting on it is (about the center of mass)
![\tau_1 = Mg\dfrac{L}{2};](https://tex.z-dn.net/?f=%5Ctau_1%20%3D%20Mg%5Cdfrac%7BL%7D%7B2%7D%3B)
therefore, the angular acceleration of rod 1 is
![\alpha_1 = \dfrac{Mg\dfrac{L}{2}}{\dfrac{1}{3}ML^2},](https://tex.z-dn.net/?f=%5Calpha_1%20%3D%20%5Cdfrac%7BMg%5Cdfrac%7BL%7D%7B2%7D%7D%7B%5Cdfrac%7B1%7D%7B3%7DML%5E2%7D%2C)
![\boxed{\alpha_1 = \dfrac{3g}{2L} }](https://tex.z-dn.net/?f=%5Cboxed%7B%5Calpha_1%20%3D%20%5Cdfrac%7B3g%7D%7B2L%7D%20%7D)
Now, for rod 2 the moment of inertia is
![I_2 = \dfrac{1}{3}(2M)(2L)^2](https://tex.z-dn.net/?f=I_2%20%3D%20%5Cdfrac%7B1%7D%7B3%7D%282M%29%282L%29%5E2)
![I_2 = \dfrac{8}{3} ML^2,](https://tex.z-dn.net/?f=I_2%20%3D%20%5Cdfrac%7B8%7D%7B3%7D%20ML%5E2%2C)
and the torque acting is (about the center of mass)
![\tau _2 = (2M)g \dfrac{(2L)}{2}](https://tex.z-dn.net/?f=%5Ctau%20_2%20%3D%20%282M%29g%20%5Cdfrac%7B%282L%29%7D%7B2%7D)
![\tau _2 = 2MgL;](https://tex.z-dn.net/?f=%5Ctau%20_2%20%3D%202MgL%3B)
therefore, the angular acceleration
is
![\alpha_2 = \dfrac{2MgL;}{\dfrac{8}{3} ML^2,}.](https://tex.z-dn.net/?f=%5Calpha_2%20%3D%20%5Cdfrac%7B2MgL%3B%7D%7B%5Cdfrac%7B8%7D%7B3%7D%20ML%5E2%2C%7D.)
![\boxed{\alpha_2 = \dfrac{3g}{4L}}](https://tex.z-dn.net/?f=%5Cboxed%7B%5Calpha_2%20%3D%20%5Cdfrac%7B3g%7D%7B4L%7D%7D)
We see here that
![\dfrac{3g}{2L} > \dfrac{3g}{4L}](https://tex.z-dn.net/?f=%5Cdfrac%7B3g%7D%7B2L%7D%20%3E%20%5Cdfrac%7B3g%7D%7B4L%7D)
therefore
![\boxed{\alpha_1 > \alpha_2.}](https://tex.z-dn.net/?f=%5Cboxed%7B%5Calpha_1%20%3E%20%5Calpha_2.%7D)
In other words , the initial angular acceleration for rod 1 is greater than for rod 2.
It will be traveling at 11m/s, because there is no friction in empty space.