Two children are riding on a merry-go-round. Child A is at a greater distance from the axis of rotation than child B. Which chil
1 answer:
Answer: Two children are riding on a marry-go-round. Child A is at a greater distance from the axis of rotation than child B. Thus, the child A, located at a greater distance from the axis of rotation have a larger tangential speed.
Explanation: To find the correct answer we have to know more about the Angular velocity of a rotating body.
<h3>What is the angular velocity?</h3>- In rotational motion, the angular velocity ω can be defined as, the change in angular displacement(Ф) per unit time (t).
- It's the revolution per second.
- The angular velocity can be expressed in terms of the tangential velocity as well as the radius of the circular path as,
- We know that the expression for the tangential velocity as,
- In the question, for both the child, the value of w will be same. Thus, the only quantity that depends on the tangential velocity will be the distance from the axis of rotation.
- The maximum will the value of V, if the r maximizes.
- Thus, child A with greater distance will have larger tangential speed.
Thus, we can conclude that, child A with greater distance will have larger tangential speed.
Learn more about the Angular velocity here:
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Answer:
a) K = 2/3 π G m ρ R₁³ / R₂ , b) U = - G m M / r
Explanation:
The law of universal gravitation is
F = G m M / r²
Part A
Let's use Newton's second law
F = m a
The acceleration is centripetal
a = v² / R₂
G m M / R₂² = m v² / R₂
v² = G M / R₂
They give us the density of the planet
ρ = M / V
V = 4/3 π R₁³
M = ρ V
M = ρ 4/3 π R₁³
v² = 4/3 π G ρ R₁³ / R₂
K = ½ m v²
K = ½ m (4/3 π G ρ R₁³ / R₂)
K = 2/3 π G m ρ R₁³ / R₂
Part B
Potential energy and strength are related
F = - dU / dr
∫ dU = - ∫ F. dr
The force was directed towards the center and the vector r outwards therefore there is an angle of 180º between the two cos 180 = -1
U- U₀ = G m M ∫ dr / r²
U - U₀ = G m M (- r⁻¹)
We evaluate for
U - U₀ = -G m M (1 / - 1 /
)
They indicate that for ri = ∞ U₀ = 0
U = - G m M / r