Answer:
mass-to-light ratio is the ratio of the mass of a body and the light output it has. it is represented by in terms of a single number and and tells us about the kind of stars making up the most luminous population in a galaxy. the mass-to-ratio of stars is greater than 1, for dark matter is 100 times high and very low for dust. higher mass-to-ratio mean that in a galaxy on average every solar mass emits a light less than the sun of the earth solar system does.
the large mass-to-light ratio shows that gas and dust is being analyzed.
Answer:
Revolutions made before attaining angular velocity of 30 rad/s:
θ = 3.92 revolutions
Explanation:
Given that:
L(final) = 10.7 kgm²/s
L(initial) = 0
time = 8s
<h3>
Find Torque:</h3>
Torque is the rate of change of angular momentum:
![T = \frac{L(final)-L(initial)}{t}\\T = \frac{10.7-0}{8}\\T=1.34 Nm](https://tex.z-dn.net/?f=T%20%3D%20%5Cfrac%7BL%28final%29-L%28initial%29%7D%7Bt%7D%5C%5CT%20%3D%20%5Cfrac%7B10.7-0%7D%7B8%7D%5C%5CT%3D1.34%20Nm)
<h3>Find Angular Acceleration:</h3>
We know that
T = Iα
α = T/I
where I = moment of inertia = 2.2kgm²
α = 1.34/2.2
α = 0.61 rad/s²
<h3>
Find Time 't'</h3>
We know that angular equation of motion is:
ω²(final) = ω²(initial) +2αθ
(30 rad/s)² = 0 + 2(0.61 rad/s²)θ
θ = (30 rad/s)²/ 2(0.61 rad/s²)
θ = 24.6 radians
Convert it into revolutions:
θ = 24.6/ 2π
θ = 3.92 revolutions
Answer:
3.24 m/s
Explanation:
Suppose that the boat sails with velocity (relative to water) direction being perpendicular to water stream. Had there been no water flow, it would have ended up 0m downstream
Therefore, the river speed is the one that push the boat 662 m downstream within 539 seconds. We can use this to calculate its magnitude
![v_r = 662 / 539 = 1.23 m/s](https://tex.z-dn.net/?f=v_r%20%3D%20662%20%2F%20539%20%3D%201.23%20m%2Fs)
So the boat velocity vector relative to the bank is the sum of of the boat velocity vector relative to the water and the water velocity vector relative to the bank. Since these 2 component vectors are perpendicular to each other, the magnitude of the total vector can be calculated using Pythagorean formula:
m/s