49. \ A rectangular plate is rotating with a constant angular speed about an axis that passes perpendicularly through one corner
1 answer:
Answer:
Explanation:
For this interesting problem, we use the definition of centripetal acceleration
a = v² / r
angular and linear velocity are related
v = w r
we substitute
a = w² r
the rectangular body rotates at an angular velocity w
We locate the points, unfortunately the diagram is not shown. In this case we have the axis of rotation in a corner, called O, in one of the adjacent corners we call it A and the opposite corner A
the distance OB = L₂
the distance AB = L₁
the sides of the rectangle
It is indicated that the acceleration in in A and B are related
we substitute the value of the acceleration
w² r_A = n r_B
the distance from the each corner is
r_B = L₂
r_A =
we substitute
\sqrt{L_1^2 + L_2^2} = n L₂
L₁² + L₂² = n² L₂²
L₁² = (n²-1) L₂²
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The book falling to the floor is described by Newton's second law and Newton's third law
Explanation:
Newton's first law of motion states that:
"An object moving at constant velocity (or at rest) keeps moving at constant velocity (or will stay at rest) unless acted upon unbalanced, external forces"
For a book falling to the floor, there is an unbalanced force acting on it (the force of gravity): therefore, we cannot apply Newton's first law.
Newton's second law of motion states that:
"The net force acting on an object is equal to the product between the object's mass, m, and its acceleration, a"
Mathematically:
For the book falling to the floor, F is the force of gravity; therefore, we can apply Newton's second law, and in this case it tells us that the book has a non-zero acceleration during its fall.
In particular, the force of gravity is (where
is the acceleration due to gravity), so the acceleration of the book is
Newton's third law of motion states that:
"When an object A exerts a force (action force) on an object B, then object B exerts an equal and opposite force (reaction force) on object A".
In this case, the Earth is exerting a force (the force of gravity) on the book during its fall: therefore, the book is also exerting a equal and opposite force (reaction force) on the Earth.
Learn more about Newton laws of motion:
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