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bezimeni [28]
3 years ago
7

A disk of mass M and radius R rotates at angular velocity ω0. Another disk of mass M and radius r is dropped on top of the rotat

ing disk such that their centers coincide. Both disks now spin at a new angular velocity ω. What is ω?
Physics
1 answer:
AleksandrR [38]3 years ago
6 0

Answer:

\omega = \frac{(R^2\omega_o}{(R^2 + r^2)}

Explanation:

As we know that there is no external torque on the system of two disc

then the angular momentum of the system will remains conserved

So we will have

L_i = L_f

now we have

L_i = (\frac{1}{2}MR^2)\omega_o

also we have

L_f = (\frac{1}{2}MR^2 + \frac{1}{2}Mr^2)\omega

now from above equation we have

(\frac{1}{2}MR^2)\omega_o  = (\frac{1}{2}MR^2 + \frac{1}{2}Mr^2)\omega

now we have

\omega = \frac{MR^2\omega_o}{(MR^2 + Mr^2)}

\omega = \frac{(R^2\omega_o}{(R^2 + r^2)}

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You and your friend throw balloons filled with water from the roof of a several story apartment house. You simply drop a balloon
Aleks [24]

Answer:

Height = 53.361 m

Explanation:

There are two balloons being thrown down, one with initial speed (u1) = 0 and the other with initial speed (u2) = 43.12

From the given information we make the following summary

u_{1} = 0m/s

t_{1} = t

u_{2} = 43.12m/s

t_{2} = (t-2.2)s

The distance by the first balloon is

D = u_{1} t_{1}  + \frac{1}{2} at_{1}^2

where

a = 9.8m/s2

Inputting the values

D = (0)t + \frac{1}{2} (9.8)t^2\\ D = 4.9t^2

The distance traveled by the second balloon

D = u_{2} t_{2}  + \frac{1}{2} at_{2}^2

Inputting the values

D = (43.12)(t-2.2)  + \frac{1}{2} (9.8)(t-2.2)^2

simplifying

D = 4.9t^2 + 21.56t -71.148

Substituting D of the first balloon into the D of the second balloon and solving

4.9t^2 = 4.9t^2 + 21.56t -71.148 \\ 21.56t = 71.148\\ t = 3.3s

Now we know the value of t. We input this into the equation of the first balloon the to get height of the apartment

D = 4.9(3.3)^2\\ D = 53.361 m

7 0
3 years ago
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