True! The mechanical advantage of the wheel and axle is equal to the ratio of the radius of the wheel over the radius of the axle.
The height of the Empire State Building is 318.00 meters. If a stone is dropped from the top of the building, what is the stone'
1 answer:
You might be interested in
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 =
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
Answer:
v = 7.67 m/s for L= 1m
Explanation:
Let's use the conservation of mechanical energy, at the highest point and the lowest point
Initial. Vertical ruler
Em₀ = mg h
Final. Just before touching the floor
= K = ½ I w²
Em₀ =
m g h = ½ I w²
The moment of inertia of a ruler that turns on one end is
I = 1/3 m L²
Let's replace
m g h = ½ (1/3 m L²) w²2
g h = 1/6 L² w²
They ask for the speed of the end so the height h is equal to the length of the ruler
g L = 1/6 L² w²
The linear and angular variables are related
v = w r
w = v / r
In this case the point of interest a in strangers r = L
g L = 1/6 L² v² / L²
v = √ 6 g L
Let's calculate
Assume that the length of the meter is L = 1 m
v = √ (6 9.8 1)
v = 7.67 m/s