Answer:
a) αA = 4.35 rad/s²
αB = 1.84 rad/s²
b) t = 3.7 rad/s²
Explanation:
Given:
wA₀ = 240 rpm = 8π rad/s
wA₁ = 8π -αA*t₁
The angle in B is:
![\theta _{B} =4\pi =\frac{1}{2} \alpha _{B} t_{1}^{2} =\frac{1}{2} (\frac{r_{A} }{r_{B} } )^{3} \alpha _{A} t_{1}^{2}=\frac{1}{2} (\frac{0.15}{0.2} )^{3} \alpha _{A} t_{1}^{2}](https://tex.z-dn.net/?f=%5Ctheta%20_%7BB%7D%20%3D4%5Cpi%20%3D%5Cfrac%7B1%7D%7B2%7D%20%5Calpha%20_%7BB%7D%20t_%7B1%7D%5E%7B2%7D%20%20%3D%5Cfrac%7B1%7D%7B2%7D%20%28%5Cfrac%7Br_%7BA%7D%20%7D%7Br_%7BB%7D%20%7D%20%29%5E%7B3%7D%20%5Calpha%20_%7BA%7D%20t_%7B1%7D%5E%7B2%7D%3D%5Cfrac%7B1%7D%7B2%7D%20%28%5Cfrac%7B0.15%7D%7B0.2%7D%20%29%5E%7B3%7D%20%5Calpha%20_%7BA%7D%20t_%7B1%7D%5E%7B2%7D)
![\alpha _{A} =8\pi (\frac{0.2}{0.15} )^{3} =59.57rad](https://tex.z-dn.net/?f=%5Calpha%20_%7BA%7D%20%3D8%5Cpi%20%28%5Cfrac%7B0.2%7D%7B0.15%7D%20%29%5E%7B3%7D%20%3D59.57rad)
![w_{B,1} =\alpha _{B} t_{1}=(\frac{0.15}{0.2} )^{3} \alpha _{A} t_{1}=0.422\alpha _{A} t_{1}](https://tex.z-dn.net/?f=w_%7BB%2C1%7D%20%3D%5Calpha%20_%7BB%7D%20t_%7B1%7D%3D%28%5Cfrac%7B0.15%7D%7B0.2%7D%20%29%5E%7B3%7D%20%5Calpha%20_%7BA%7D%20t_%7B1%7D%3D0.422%5Calpha%20_%7BA%7D%20t_%7B1%7D)
The velocity at the contact point is equal to:
![v=r_{A} w_{A} =0.15*(8\pi -\alpha _{A} t_{1})=1.2\pi -0.15\alpha _{A} t_{1}](https://tex.z-dn.net/?f=v%3Dr_%7BA%7D%20w_%7BA%7D%20%3D0.15%2A%288%5Cpi%20-%5Calpha%20_%7BA%7D%20t_%7B1%7D%29%3D1.2%5Cpi%20-0.15%5Calpha%20_%7BA%7D%20t_%7B1%7D)
![v=r_{B} w_{B} =0.2*(0.422\alpha _{A} t_{1})=0.0844\alpha _{A} t_{1}](https://tex.z-dn.net/?f=v%3Dr_%7BB%7D%20w_%7BB%7D%20%3D0.2%2A%280.422%5Calpha%20_%7BA%7D%20t_%7B1%7D%29%3D0.0844%5Calpha%20_%7BA%7D%20t_%7B1%7D)
Matching both expressions:
![1.2\pi -0.15\alpha _{A} t_{1}=0.0844\alpha _{A} t_{1}\\\alpha _{A} t_{1}=16.09rad/s](https://tex.z-dn.net/?f=1.2%5Cpi%20-0.15%5Calpha%20_%7BA%7D%20t_%7B1%7D%3D0.0844%5Calpha%20_%7BA%7D%20t_%7B1%7D%5C%5C%5Calpha%20_%7BA%7D%20t_%7B1%7D%3D16.09rad%2Fs)
b) The time during which the disks slip is:
![t_{1} =\frac{\alpha _{A} t_{1}^{2}}{\alpha _{A} t_{1}} =\frac{59.574}{16.09} =3.7s](https://tex.z-dn.net/?f=t_%7B1%7D%20%3D%5Cfrac%7B%5Calpha%20_%7BA%7D%20t_%7B1%7D%5E%7B2%7D%7D%7B%5Calpha%20_%7BA%7D%20t_%7B1%7D%7D%20%3D%5Cfrac%7B59.574%7D%7B16.09%7D%20%3D3.7s)
a) The angular acceleration of each disk is
![\alpha _{A}=\frac{\alpha _{A} t_{1}}{t_{1} } =\frac{16.09}{3.7} =4.35rad/s^{2} (clockwise)](https://tex.z-dn.net/?f=%5Calpha%20_%7BA%7D%3D%5Cfrac%7B%5Calpha%20_%7BA%7D%20t_%7B1%7D%7D%7Bt_%7B1%7D%20%7D%20%3D%5Cfrac%7B16.09%7D%7B3.7%7D%20%3D4.35rad%2Fs%5E%7B2%7D%20%28clockwise%29)
![\alpha _{B}=(\frac{0.15}{0.2} )^{3} *4.35=1.84rad/s^{2} (clockwise)](https://tex.z-dn.net/?f=%5Calpha%20_%7BB%7D%3D%28%5Cfrac%7B0.15%7D%7B0.2%7D%20%29%5E%7B3%7D%20%2A4.35%3D1.84rad%2Fs%5E%7B2%7D%20%28clockwise%29)
Answer:
to the left the first answer can be "Consumer" and under it can go "plant"
to the right the first answer on the top can be "Carnivore" under it can go "Herbivore" and under it can go "Producer"
I just had this question and its right
Answer:
A
Explanation:
A nonpolar molecule has no separation of charge, so no positive or negative poles are formed. In other words, the electrical charges of nonpolar molecules are evenly distributed across the molecule. Nonpolar molecules tend to dissolve well in nonpolar solvents, which are frequently organic solvents.
Answer:
135° (degrees)
Explanation:
The Earth rotates 360° in about 24 h
How many degrees in 1 hour
![360^{\circ}=24\ h\\\Rightarrow 1\ h=\frac{360}{24}\\\Rightarrow 1\ h=15^{\circ}](https://tex.z-dn.net/?f=360%5E%7B%5Ccirc%7D%3D24%5C%20h%5C%5C%5CRightarrow%201%5C%20h%3D%5Cfrac%7B360%7D%7B24%7D%5C%5C%5CRightarrow%201%5C%20h%3D15%5E%7B%5Ccirc%7D)
So, in 1 hour the Earth rotates 15 degrees. This means that a person would have to reset their watch by 1 hour after travelling 15 degrees
In 9 hours
![9\ h=9\times 15^{\circ}=135^{\circ}\\\Rightarrow 9\ h=135^{\circ}](https://tex.z-dn.net/?f=9%5C%20h%3D9%5Ctimes%2015%5E%7B%5Ccirc%7D%3D135%5E%7B%5Ccirc%7D%5C%5C%5CRightarrow%209%5C%20h%3D135%5E%7B%5Ccirc%7D)
So, a person would have to travel 135 degrees in order to reset their watch by 9 hours.
Energy is neither created nor destroyed
E in = E out
750 J in so 750 J out