Consider light energy that is momentarily absorbed in glass and then re-emitted. Compared to the absorbed light, the frequency o
1 answer:
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To solve this problem we will use the concepts related to gravitational acceleration and centripetal acceleration. The equality between these two forces that maintains the balance will allow to determine how the rigid body is consistent with a spherically symmetric mass distribution of constant density. Let's start with the gravitational acceleration of the Star, which is
Here
Mass inside the orbit in terms of Volume and Density is
Where,
V = Volume
Density
Now considering the volume of the star as a Sphere we have
Replacing at the previous equation we have,
Now replacing the mass at the gravitational acceleration formula we have that
For a rotating star, the centripetal acceleration is caused by this gravitational acceleration. So centripetal acceleration of the star is
At the same time the general expression for the centripetal acceleration is
Where is the orbital velocity
Using this expression in the left hand side of the equation we have that
Considering the constant values we have that
As the orbital velocity is proportional to the orbital radius, it shows the rigid body rotation of stars near the galactic center.
So the rigid-body rotation near the galactic center is consistent with a spherically symmetric mass distribution of constant density
Answer:
Assumption: the air resistance on this ball is negligible. Take .
a. The momentum of the ball would be approximately two seconds after it is tossed into the air.
b. The momentum of the ball would be approximately three seconds after it reaches the highest point (assuming that it didn't hit the ground.) This momentum is smaller than zero because it points downwards.
Explanation:
The momentum of an object is equal its mass
times its velocity
. That is:
.
Assume that the air resistance on this ball is negligible. If that's the case, then the ball would accelerate downwards towards the ground at a constant . In other words, its velocity would become approximately
more negative every second.
The initial velocity of the ball is . After two seconds, its velocity would have become
. The momentum of the ball at that time would be around
.
When the ball is at the highest point of its trajectory, the velocity of the ball would be zero. However, the ball would continue to accelerate downwards towards the ground at a constant . That's how the ball's velocity becomes negative.
After three more seconds, the velocity of the ball would be . Accordingly, the ball's momentum at that moment would be
.