Hi there!
a.
We can use the initial conditions to solve for w₀.
It is given that:
We are given that at t = 0, ω = 3.7 rad/sec. We can plug this into the equation:
Now, we can solve for sigma using the other given condition:
b.
The angular acceleration is the DERIVATIVE of the angular velocity function, so:
c.
The angular displacement is the INTEGRAL of the angular velocity function.
Convert this to rev:
d.
We can begin by solving for the time necessary for the angular speed to reach 0 rad/sec.
Evaluate the improper integral:
Convert to rev:
Answer:
The average surface temperature decreases the further you get from the Sun because the more distant planets receive less energy/heat/sunlight per square meter of their surface. This is because the energy from the Sun spreads out (becomes less concentrated) as you travel further from the source/Sun.
Explanation:
I think the answer will be A
The distance an object falls, from rest, in gravity is
D = (1/2) (G) (T²)
'T' is the number seconds it falls.
In this problem,
0.92 meter = (1/2) (9.8) (T²)
Divide each side by 4.9 : 0.92 / 4.9 = T²
Take the square root
of each side: √(0.92/4.9) = T
0.433 sec = T
The horizontal speed doesn't make a bit of difference in
how long it takes to reach the floor. BUT ... if you want to
know how far from the table the pencil lands, you can find
that with the horizontal speed.
The pencil is in the air for 0.433 second.
In that time, it travels
(0.433s) x (1.4 m/s) = 0.606 meter
from the edge of the table.