a) 
b) 
Explanation:
a)
Since there are no external torques acting on the system, the total angular momentum must remain constant.
At the beginning, the merry-go-round and the girl are at rest, so the initial angular momentum is zero:
Later, after the girl throws the rock, the angular momentum will be:
where:
is the moment of inertia of the merry-go-round
is the moment of inertia of the girl, where
M is the mass of the girl
R is the distance of the girl from the axis of rotation
is the angular speed of the merry-go-round and the girl
is the angular momentum of the rock, where
m is the mass of the rock
v is its velocity
Since the total angular momentum is conserved,
So we find:
And the negative sign indicates that the disk rotates in the direction opposite to the motion of the rock.
b)
The linear speed of a body in rotational motion is given by
where
is the angular speed
r is the distance of the body from the axis of rotation
In this problem, for the girl, we have:
is the angular speed
is the distance of the girl from the axis of rotation
Therefore, her linear speed is:
1). Sequence from the Sun:
Inner planets:
Mercury
Venus
Earth
Mars
Outer planets:
Jupiter
Saturn
Uranus
Neptune
2). The farther a planet is from the sun, the longer it takes
to orbit the sun. Mercury ... 88 days. Earth ... 365 days.
Jupiter ... 12 years. Neptune ... 165 years.
3). Mercury & Venus ... no moons
Earth - 1
Mars - 2
Jupiter - more than 65
4). Mercury ... cratered, no atmosphere
Venus ... cratered, thick cloudy atmosphere
Mars ... dry, cratered, slight atmosphere, like 1% or Earth's
Jupiter, Saturn, Uranus, Neptune
We can't see any surface. If any of them even
HAS a surface, it's thousands of miles under a
thick atmosphere of methane gas.
5). Missing from the list
6). Here's a list from the biggest planet to the smallest one.
The numbers in parentheses are the radius of the planet --
half of the diameter:
Jupiter (69,911 km / 43,441 miles) – 1,120% the size of Earth
Saturn (58,232 km / 36,184 miles) – 945% the size of Earth
Uranus (25,362 km / 15,759 miles) – 400% the size of Earth
Neptune (24,622 km / 15,299 miles) – 388% the size of Earth
Earth (6,371 km / 3,959 miles)
Venus (6,052 km / 3,761 miles) – 95% the size of Earth
Mars (3,390 km / 2,460 miles) – 53% the size of Earth
Mercury (2,440 km / 1,516 miles) – 38% the size of Earth
7). At least seven of the planets rotate in the same direction.
There's something different about one of them ... it may be Uranus
but I'm not sure. You'll have to look this up.
8). Saturn has the famous rings, that you can almost see
with only binoculars.
Spacecraft sent to observe the outer planets have detected
very thin rings around Uranus and Neptune.
9). Included in #6.
10). I don't have complete info. Generally, the closer the planet
is to the sun, the hotter it is. But there are a few exceptions.
I think Venus ... the second one from the sun, is actually hotter
than Mercury.
11). Just about every language has its own name for each planet.
12). "Terrestrial" means "like Earth" ("Terra").
The terrestrial planets are the ones that have solid surfaces
and are made of rock.
Mercury, Venus, Earth, and Mars.
13). "Jovian" means "like Jupiter".
Either no solid surface, or very small, inside a big deep gas ball.
Jupiter, Saturn, Uranus, Neptune.
1=6, 2=8
I hope this helped
Answer:
(a) 3.44 x 10^-3 m^3/s
(b) 8.4 m/s
Explanation:
area of water line, A = 5.29 x 10^-3 m
number of holes, N = 15
Speed of water in line, V = 0.651 m/s
(a) Volume flow rate is given by
V = area of water line x speed of water in water line
V = 5.29 x 10^-3 x 0.651 = 3.44 x 10^-3 m^3/s
(b) area of one hole, a = 4.13 x 10^-4 m
Let v be the velocity of water in each hole
According to the equation of continuity
A x V = a x v
5.29 x 10^-3 x 0.651 = 4.1 x 10^-4 x v
v = 8.4 m/s
