Answer:
Explanation:
The magnitude of the acceleration makes an angle of 30° with the tangential velocity.
Resolving the acceleration to tangential and radial acceleration
at = aCos30 = √3a/2
ar = aSin30 = ½a
a = 2•ar
Then, the tangential acceleration is the linear acceleration, so the relationship between the tangential acceleration and angular acceleration is given as:
at = Rα
Then, α = at/R
since at = √3a/2
Then, α = √3 at/2R, equation 1
The radial acceleration is given as
ar = ω²R
Note that, at² + ar² = a²
at = √(a²-ar²)
Back to equation 1
α = √3 at/2R
α = √3√(a²-ar²)/2R
α = √3√(a²-(w²R)²)/2R
α = √3(a²-w⁴R²) / 2R
Also, a = 2•ar = 2w²R
Then,
α = √3((2w²R)²-w⁴R²) / 2R
α = √3(4w⁴R²-w⁴R²) / 2R
α = √3(3w⁴R²) / 2R
α = √9w⁴R² / 2R
α = 3w²R / 2R
α = 3w²/2
Answer:
241,274.32 inches
Explanation:
How far will he travel if the rear wheel makes 1200 revolutions on the road?
Since the rear wheel makes one revolution in the distance of a circumference of a circle, C with diameter, d = 16 inches
C = πd²/4
So, the distance, travelled in 1200 revolutions is D = 1200 × C = 1200πd²/4
Substituting d = 16 into D, we have
D = 1200πd²/4
D = 1200π(16)²/4
D = 76800π
D = 241,274.32 inches
Answer:
The value is 
Explanation:
From the question we are told that
The saturation density of air is 
The temperature for this saturation density to occur 
The relative humidity at this temperature is 
Generally the relative humidity is mathematically represented as
Here H represents humidity
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