Answer:
the moment of inertia of the wheel is 0.408 kg.m²
Explanation:
Given;
tangential force applied to the wheel, f = 90 N
radius of the wheel, r = 0.15 m
initial angular speed of the wheel, ω₁ = 0
final angular speed of the wheel, ω₂ = 14.3 rev/s
time of motion of the wheel, t = 2.72 s
The tangential acceleration of the wheel is calculated as;
where;
is the angular acceleration
The mass of the wheel is calculated as;
F = ma
m = F/a
m = (90)/(4.96)
m = 18.15 kg
The moment of inertia of the wheel is calculated as;
I = mr²
I = 18.15 x (0.15)²
I = 0.408 kg.m²
Therefore, the moment of inertia of the wheel is 0.408 kg.m²
Explanation:
There is no any direct relationship between the frequency of a sound relative the intensity of the sound.
Frequency is a perception of pitch of the sound whereas intensity determines the loudness of the sound. Intensity is proportional to amplitude of the sound.
So, it would be hard to determine how much more intense is a 6000 Hz tone than a 80 Hz tone.
Reflection<span> is bouncing off a barrier or interface. </span>Refraction<span> is bending of light's path at the interface between two media. All angles are to be measured from the normal to the surface. The incident angle and the reflected angle are equal. The refracted angle may be larger or smaller than the incident angle.</span>
<span>The </span>index of refraction, n, is a ratio that compares the speed of light in a vacuum to the speed of light in another medium.
n = c/v where c = speed of light in a vacuum = 3x108<span> m/s</span>
The speed of light in all other media is less than in a vacuum. Therefore, n is always larger than one. It may be thought of as the measure of the slowness of light in a medium: the slower light travels in medium, the larger n will be for that medium. Since n divides speed by speed it has no units.
The frequency of light does not change as it enters a different medium, but its wavelength does. Since
v = fL where f = frequency and L = wavelength
then
v1/v2<span> = L</span>1/L<span>2
</span>EXAMPLE
1.
a. What is the speed of light in water, if water's index of refraction is 1.33?
b. If the wavelength of a ray of light in a vacuum is 1x10-6 m, what is its wavelength in water?
ANSWER
1.
a. n = c/v
1.33 = (3 X 108 m/s)/v
v = 2.26x108 m/s
b. v1/v2 = L1/L2
(2.26x108 m/s)/(3x108 m/s) = L1/(1x10-6 m)
L1 = 7.52x10-7 m
Answer:
The angular speed (in rev/s) when her arms and one leg open outward is 1.161 rev/s
Explanation:
Given;
moment of inertia of a skater with arms out, = 3.1 kg.m²
moment of inertia of a skater with arms in, = 0.9 kg.m²
inward angular speed, = 4 rev/s
The angular momentum of the skater when her arms are out and one leg extended is equal to her angular momentum when her arms and legs are in.
Therefore, the angular speed (in rev/s) when her arms and one leg open outward is 1.161 rev/s
Answer:
R = 103.7 N, 31.6° above x-axis
Explanation:
First we find the x components of all the forces:
F1x = F1 Cos 60°
F1x = (100 N)(Cos 60°)
F1x = 50 N
F2x = F2 Cos 140°
F2x = (200 N)(Cos 140°)
F2x = -153.2 N
F3x = F3 Cos 320°
F3x = (250 N)(Cos 320°)
F3x = 191.5 N
So, the x component of resultant will be the sum of the x component of each force:
Rx = F1x + F2x + F3x
Rx = 50 N - 153.2 N + 191.5 N
Rx = 88.3 N
Now we find the y components of all the forces:
F1y = F1 Sin 60°
F1y = (100 N)(Sin 60°)
F1y = 86.6 N
F2y = F2 Sin 140°
F2y = (200 N)(Sin 140°)
F2y = 128.5 N
F3y = F3 Sin 320°
F3y = (250 N)(Sin 320°)
F3y = -160.7 N
So, the y component of resultant will be the sum of the y component of each force:
Ry = F1y + F2y + F3y
Ry = 86.6 N + 128.5 N - 160.7 N
Ry = 54.4 N
Hence, the magnitude of resultant force will be:
|R| = √(Rx² + Ry²)
|R| = √[(88.3 N)² + (54.4 N)²]
|R| = √10756.25 N²
|R| = 103.7 N
And the direction θ will be:
θ = tan⁻¹(Ry/Rx)
θ = tan⁻¹(54.4/88.3)
θ = 31.6° above x-axis
Hence, the resultant vector will be:
<u>R = 103.7 N, 31.6° above x-axis</u>