a) 6.25 rad/s
The law of conservation of angular momentum states that the angular momentum must be conserved.
The angular momentum is given by:
where
I is the moment of inertia
is the angular speed
Since the angular momentum must be conserved, we can write
where we have
is the initial moment of inertia
is the initial angular speed
is the final moment of inertia
is the final angular speed
Solving for , we find
b) 28.1 J and 35.2 J
The rotational kinetic energy is given by
where
I is the moment of inertia
is the angular speed
Applying the formula, we have:
- Initial kinetic energy:
- Final kinetic energy:
Answer:
1.2 m/s^2
Explanation:
acceleration = change in velocity / change in time
= 6 m/s / 5 sec = 1.2 m/s^2
singer when you went to leaving
Answer:
13.02 m/s the velocity and 86.92 degrees the direction relative to ground
Explanation:
We need to add velocities in vector addition to find the resultant velocity "" of the balloon (the 13 m/s and the 0.7 m/s).
The velocities are at 90 degrees from each other (one pointing up and the other to the East). Notice from the attached image that the resultant velocity vector (picture in red) is actually the hypotenuse of a right angle triangle.
So we use Pythagoras to find the length (magnitude) of the resultant velocity vector:
we can round the answer to 13.02 m/s
Now we need to find the angle that this new vector makes with the ground by using the definition of tangent of an angle that relates the two quantities that we just added:
So we round it to 86.92 degrees