Answer:
ω = √((3g/L)*(1 - Cos θ))
Step-by-step explanation:
We need to apply the Principle of Conservation of mechanical energy as follows
Ei = Ef ⇒ Ki + Ui = Kf + Uf
In the vertical position
ωi = 0 ⇒ Ki = 0
yi = L/2 ⇒ Ui = m*g*L/2
We can get the rotational inertia I using the formula
I = m*L²/3
then
Kf = I*ω²/2 = (m*L²/3)*ω²/2 = m*L²*ω²/6
Now, we obtain the potential energy Uf as follows
Uf = m*g*y
where
y = (L/2)*Cos θ
⇒ Uf = m*g*(L/2)*Cos θ
Now, we have
Ui = Kf + Uf
⇒ m*g*L/2 = (m*L²*ω²/6) + (m*g*(L/2)*Cos θ)
⇒ ω² = (3g/L)*(1 - Cos θ)
⇒ ω = √((3g/L)*(1 - Cos θ))
We need to know the coefficient of static friction in order to get the value of theta where slip takes place.
The answer is 3 to subtract the fractions, find the LCD and then combine
Answer:
Ratios are proportional if they represent the same relationship. One way to see if two ratios are proportional is to write them as fractions and then reduce them. If the reduced fractions are the same, your ratios are proportional.
Step-by-step explanation:
Answer:
a
Step-by-step explanation:
Greatest Common Factor is the "biggest" number that each have in common
20 a bbb + 16 aa b + a
the only thing all three have in commom is the "a"
Answer:
The length of the sides of the square is 9.0015
Step-by-step explanation:
Given
The diagonal of a square = 12.73
Required
The length of its side
Let the length and the diagonal of the square be represented by L and D, respectively.
So that
D = 12.73
The relationship between the diagonal and the length of a square is given by the Pythagoras theorem as follows:
Solving further, we have
Divide both sides by 2
Take Square root of both sides
Reorder
Now, the value of L can be calculated by substituting 12.73 for D
(Approximated)
Hence, the length of the sides of the square is approximately 9.0015
