Answer:
w = 4,786 rad / s
, f = 0.76176 Hz
Explanation:
For this problem let's use the concept of angular momentum
L = I w
The system is formed by the two discs, during the impact the system remains isolated, we have the forces are internal, this implies that the external torque is zero and the angular momentum is conserved
Initial Before sticking
L₀ = 0 + I₂ w₂
Final after coupling
= (I₁ + I₂) w
The moments of inertia of a disk with an axis of rotation in its center are
I = ½ M R²
How the moment is preserved
L₀ = ![L_{f}](https://tex.z-dn.net/?f=L_%7Bf%7D)
I₂ w₂ = (I₁ + I₂) w
w = w₂ I₂ / (I₁ + I₂)
Let's reduce the units to the SI System
d₁ = 60 cm = 0.60 m
d₂ = 40 cm = 0.40 m
f₂ = 200 min-1 (1 min / 60 s) = 3.33 Hz
Angular velocity and frequency are related.
w₂ = 2 π f₂
w₂ = 2π 3.33
w₂ = 20.94 rad / s
Let's replace
w = w₂ (½ M₂ R₂²) / (½ M₁ R₁² + ½ M₂ R₂²)
w = w₂ M₂ R₂² / (M₁ R₁² + M₂ R₂²)
Let's calculate
w = 20.94 8 0.40² / (12 0.60² + 8 0.40²)
w = 20.94 1.28 / 5.6
w = 4,786 rad / s
Angular velocity and frequency are related.
w = 2π f
f = w / 2π
f = 4.786 / 2π
f = 0.76176 Hz
We've seen this introduction to a question posted several times before here on Brainly, but it always stops right there. What is the question ? ? ?
Answer:
Which of the following was not a reaction to John Brown's execution because of his failed raid on Harper's Ferry ???????
Explanation:
The bigger the object the greater the gravitational pull, so the farther away the big object is its gravitational force begins to decrease. Refer to the picture for more explanation.
Answer:
Explanation:
From the given information:
radius = 15 m
Time T = 23 s
a) Speed (v) = ![\dfrac{2 \pi r}{T}](https://tex.z-dn.net/?f=%5Cdfrac%7B2%20%5Cpi%20r%7D%7BT%7D)
![v = \dfrac{2\times \pi \times 15}{23}](https://tex.z-dn.net/?f=v%20%3D%20%5Cdfrac%7B2%5Ctimes%20%5Cpi%20%5Ctimes%2015%7D%7B23%7D)
v = 4.10 m/s
b) The magnitude of the acceleration is:
![a = \dfrac{v^2}{r} \\ \\ a = \dfrac{(4.10)^2}{15}](https://tex.z-dn.net/?f=a%20%3D%20%5Cdfrac%7Bv%5E2%7D%7Br%7D%20%5C%5C%20%5C%5C%20a%20%3D%20%5Cdfrac%7B%284.10%29%5E2%7D%7B15%7D)
a = 1.12 m/s²
c) True weight = mg
Apparent weight = normal force
From the top;
the normal force = upward direction,
weight is downward as well as the acceleration.
true weight - normal force = ma
apparent weight =mg - ma
![\dfrac{apparent \ weight}{true \ weight} = \dfrac{(mg - ma)}{(mg)}](https://tex.z-dn.net/?f=%5Cdfrac%7Bapparent%20%5C%20weight%7D%7Btrue%20%5C%20%20weight%7D%20%3D%20%5Cdfrac%7B%28mg%20-%20ma%29%7D%7B%28mg%29%7D)
![=1- \dfrac{1.12}{9.8}](https://tex.z-dn.net/?f=%3D1-%20%5Cdfrac%7B1.12%7D%7B9.8%7D)
= 0.886 m/s²
d)
From the bottom;
acceleration is upward, so:
apparent weight - true weight = ma
apparent weight = true weight + ma
![\dfrac{apparent \ weight }{true \ weight} =\dfrac{ mg + ma}{mg}](https://tex.z-dn.net/?f=%5Cdfrac%7Bapparent%20%5C%20weight%20%7D%7Btrue%20%5C%20weight%7D%20%3D%5Cdfrac%7B%20mg%20%2B%20ma%7D%7Bmg%7D)
![\dfrac{apparent \ weight }{true \ weight} =1+ \dfrac{a}{g} \\ \\ = 1 + \dfrac{1.12}{9.8}](https://tex.z-dn.net/?f=%5Cdfrac%7Bapparent%20%5C%20weight%20%7D%7Btrue%20%5C%20weight%7D%20%3D1%2B%20%5Cdfrac%7Ba%7D%7Bg%7D%20%5C%5C%20%5C%5C%20%3D%201%20%2B%20%5Cdfrac%7B1.12%7D%7B9.8%7D)
![= 1 + \dfrac{1.12}{9.8} \\ \\](https://tex.z-dn.net/?f=%3D%201%20%2B%20%5Cdfrac%7B1.12%7D%7B9.8%7D%20%5C%5C%20%5C%5C)
= 1.114 m/s²