Question in proper order
The rotational kinetic energy term is often called the <em>kinetic energy </em><em>in</em> the center of mass, while the translational kinetic energy term is called the <em>kinetic energy </em><em>of</em> the center of mass.
You found that the total kinetic energy is the sum of the kinetic energy in the center of mass plus the kinetic energy of the center of mass. A similar decomposition exists for angular and linear momentum. There are also related decompositions that work for systems of masses, not just rigid bodies like a dumbbell.
It is important to understand the applicability of the formula
Which of the following conditions are necessary for the formula to be valid?
a. The velocity vector must be perpendicular to the axis of rotation
b.The velocity vector must be perpendicular or parallel to the axis of rotation
c. The moment of inertial must be taken about an axis through the center of mass
Answer:
Option c
Explanation:
The first two conditions are untrue, this is because, you can have rotation in any direction and translation in any direction of any collection of masses. Rotational and translational velocities of masses do not depend on each other
The last statement is true because by definition, the moment of inertia, which is a measure of reluctance, is usually taken about a reference point which is the center of mass
Answer:
Explanation:
The Hi line of the Balmer series is emitted in the transition from n = 3 to n = 2 i.e. and
The wavelength of Hi line of the Balmer series is given by :
So, the wavelength for this line is 550 nm. Hence, this is the required solution.
Answer:
Yes, the paths of the two particles cross.
Location of path intersection = ( 1 , 2 , 3)
Explanation:
In order to find the point of intersection, we need to set both locations equal to one another. It should be noted however, that the time for each particle can vary as we are finding the point where the <u>paths</u> meet, not the point where the particles meet themselves.
So, we can name the time of the first particle , and the time of the second particle
.
Setting the locations equal, we get the following equations to solve for and
:
Equation 1
Equation 2
Equation 3
Solving these three equations simultaneously we get:
2 seconds
4 seconds
Since, we have an answer for when the trajectories cross, we know for a fact that they indeed do cross.
The point of crossing can be found by using the value of or
in the location matrices. Doing this for the first particle we get:
Location of path intersection = ( -1 + 2 , 4 - 2 , -1 + 2(2) )
Location of path intersection = ( 1 , 2 , 3)