All of the waves in the electromagnetic spectrum are _______ waves.
1 answer:
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Answer:
The angle of rotation given is incorrect, the correct function to have a balanced unit is
θ(t) = (1.10 rad/s)t + (6.30 rad/s²)t²
Explanation:
Given that,
Radius of disk is
R = 0.4m
Mass of disk
M = 30kg
The angle of rotation is a function of time and it is given as
θ(t) = (1.10 rad/s)t + (6.30 rad/s²)t²
What is linear angular acceleration "a" when it rotates 0.1rev
θ = 0.1 rev
1 rev = 2πrad
θ = 0.1 × 2πrad = 0.63 rad
Let calculate the time it revolves 0.63rad
θ(t) = (1.10 rad/s)t + (6.30 rad/s²)t².
0.63 = 1.1t + 6.3t²
6.3t² + 1.1t - 0.63 = 0
Solving this quadratic equation using formula method
t = [-b±√(b²-4ac)]/2a
a = 6.3 b = 1.1 c = -0.63
t = [-1.1 ± √(1.1²-4×6.3×-0.63)]/2×6.3
t = -1.1±√(1.21+15.876) / 12.6
t = -1.1 ± 4.13 / 12.6
Let discard the negative time
So, t = (-1.1 + 4.13) / 12.6
t = 0.24 s
Now,
Angular velocity can be determine using
ωz = dθ / dt
ωz = 1.1 + 12.6t, since t = 0.24
ωz = 1.1 + 12.6(0.24)
ωz = 4.124 rad/s
Angular acceleration can be determine using
αz = dωz/dt
αz = 12.6 rad/s²
The radial acceleration can be determined using
ar = ωz²•R
ar = 4.124² × 0.4
ar = 6.8 m/s²
Also, the tangential Acceleration is related to angular acceleration using
at = αz • R
at = 12.6 × 0.4
at = 5.04 m/s²
Then, the magnitude of the resultant acceleration can be calculated using
a = √(ar² + at²)
a = √(6.8² + 5.04²)
a = √71.64
a = 8.46 m/s²
Direction
β = Arctan(at/ar)
β = Arctan(5.04/6.8)
β = 36.54
This is the direction from the origin
But it has already revolve 0.1rev
1 rev = 360°
Then, θ = 0.1° = 360 × 0.1 = 36°
Direction = β — θ
Then, it direction is 36.54 — 54° = 0.54°
The direction is 0.54°
Check attachment for direction understanding
