Answer:
a) I = 0.0198 kg m²
, b) I = 21.85 kg m²
Explanation:
For this exercise we will use the definition of moment of inertia
I = ∫ r² dm
For body with high symmetry they are tabulated
sphere I = 2/5 m r²
bar with respect to center of mass I = 1/12 m L²
let's calculate the mass of each body
bar
ρ = m / V
m = ρ V
m = ρ l w h
where we are given the density of the bar rho = 32840 kg / m³ and its dimensions 1 m, 0.8 cm and 4 cm
m = 32820 1 0.008 0.04
m = 10.5 kg
Sphere
M = ρ V
V = 4/3 pi r³
M = rgo 4/3 π r³
give us the density 37800 kg / m³ and the radius of 5 cm
M = 37800 4/3 π 0.05³
M = 19.8 kg
a) asks us for the moment of inertia of the sphere with respect to its center of mass
I = 2/5 M r²
I = 2/5 19.8 0.05²
I = 0.0198 kg m²
b) the moment of inertia with respect to the turning point, for this we will use the theorem of parallel axes
I = I_cm + M d2
where d is the distance from the body to the point of interest
I_cm = 0.0198 kg m²
the distance to the pivot point is
l = length of the bar + radius of the sphere
l = 1 + 0.05 = 1.005 m
I = 0.0198 + 19.8 1.05²
I = 21.85 kg m²
Answer:
A brighter light
Explanation:
Light waves travel through space via light particles called photons. This particles have in essence 2 properties: 1. Amplitude and 2.Frequency. The first one has to do with the intensity of light we see and the second one has to do with the energy (color). If we change only the amplitude, we will see a lighter or darker light and will keep the same color in all amplitude changes. But if we modify the frequency, the intensity will keep the same and the color changes as we move into the light spectrum.
Thus, increasing the amplitude, we will perceive a brigher light.
Answer: 12.0 m/s^2
Explanation:
Let
be the angular acceleration of the end of the rod
Taking torque about the link, we have:

Torque is also given in terms of moment of inertia of the rod and its angular acceleration i.e.

From equations (i) and (ii) we have:

The acceleration of the end of the rod farthest from the link is given by:

The combustion of fossil fuels is releasing more co2 into the atmosphere then what would occur naturally