. Conservation along the horizontal using a bicycle wheel: Stand on the platform holding a bicycle wheel with its axis horizonta
1 answer:
Answer:
w = I₂ / (I₁ -I₂) w₀ , L₂ = 2 L₁
Explanation:
This is an angular momentum exercise,
L = I w
where bold indicates vectors
We must define the system as formed by the bicycle wheel, the platform, we create a reference system with the positive sign up
At the initial moment the wheel is turning and the platform is without rotation
The initial angle moment is
Lo = L₂ = I₂ w₀
L₁ is the angular momentum of the platform and L₂ is the angular momentum of the wheel.
In the Final moment, when the wheel was turned,
= L₁ - L₂
L_{f} = (I₁ - I₂) w
the negative sign of the angular momentum of the wheel is because it is going downwards since the two go with the same angular velocity
as all the force are internal, and there is no friction the angular momentum is conserved,
L₀ =L_{f}
I₂ w₀ = (I₁ -I₂) w
w = I₂ / (I₁ -I₂) w₀
we can see that the system will complete more slowly
we can also equalize the angular cognition equations
L₀ = Lf
L₁ = L₂-L₁
L₂ = 2 L₁
In this part we can see that the change in the angular momentum of the platform is twice the change in the angular momentum of the wheel.
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An example that illustrates the difference is the circular motion
Explanation:
Let's start by reminding the definition of the two quantities:
- Speed is a scalar quantity that tells "how fast" an object is moving, regardless of its direction of motion.
Speed can be calculate as:
where:
d is the distance travelled
t is the time taken
- Velocity is instead a vector quantity, given by:
where;
d is the displacement of the object (displacement is a a vector connecting the initial position to the final position of motion)
t is the time taken
Since it is a vector, velocity has both a magnitude and a direction, therefore it also takes into account the direction of motion of the object.
For an object in motion in a straight line, speed and velocity are the same. However, this is not always the case.
In fact, an example of motion in which the two quantities are different is the circular motion. Consider for example the object making one complete revolution along the circle. Therefore, its average speed is the ratio between the length of the perimeter (the distance) divided by the time taken:
where r is the radius of the circle.
However, the displacement of the object is zero (because the object returns to the starting point), and so the average velocity is also zero:
Learn more about speed and velocity:
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