Answer:
w = w₀ M / (M + 2m)
Explanation:
This exercise can be solved using the concepts of conservation of angular momentum
L = I w
Let's write in angular momentum in two points
Initial. Before impact
L₀ = I w₀
Final. After the rock has stuck
= I w + (m r²) w
The system is formed by the disk and the rock, so that the forces and moments during the crash are internal and the angular momentum is preserved
L₀ =
I w₀ = (I + m r²) w
w = w₀ I / (I + m r²)
The roundabout is a disk so its moment of inertia is
I = ½ M r²
w = w₀ ½ Mr² / (½ M r² + mr²)
w = w₀ ½ M / (½ M + m)
w = w₀ ½ M2 / (M + 2m)
w = w₀ M / (M + 2m)
Explanation:
It is given that,
Mass of lithium,
It is accelerated through a potential difference, V = 224 V
Uniform magnetic field, B = 0.724 T
Applying the conservation of energy as :
q is the charge on an electron
v = 78608.58 m/s
To find the radius of the ion's path in the magnetic field. The centripetal force is balanced by the magnetic force as :
r = 0.0078 meters
So, the radius of the path of the ion is 0.0078 meters. Hence, this is the required solution.