Falling rotating sphere and displacements

In summary, the student is trying to find the point P and the center of C after 0.5 seconds from their initial position. They know the two positions of the sphere and where P is at each position. They then work out PP' and CC' and find the ratio.
  • #1
LoveBoy
44
1

Homework Statement


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Homework Equations


How to locate the point P and C after 0.5s from their initial position ?

The Attempt at a Solution


Well i don't know whether it would be correct way to start the problem i.e find the centripetal acceleration .
 
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  • #2
You can find how far C moves in 0.5 sec, since it is the centre of gravity of the sphere.
So you know the two positions of the sphere and where P is at each position.
Then simply work out PP' and CC' and find the ratio.
 
  • #3
To compute for the displacement of point C use the equation for free falling bodies. As for point P, compute for the angle using the angular velocity and you will find that it has traveled all the way to the other side of the sphere (be careful here as you are dealing with displacement, not total distance). With that you should be able to get the ratio.
 
  • #4
As C is in free fall condition,so
0Vs5NZr.png

rickz02 said:
As for point P, compute for the angle using the angular velocity and you will find that it has traveled all the way to the other side of the sphere (be careful here as you are dealing with displacement, not total distance).
How to find angle using angular velocity ?
 
  • #5
distance = velocity x time so angle = angular velocity x time

You can work that out from the question, because the angular velocity is given as radians per second. So if you multiply it by seconds, you will get radians.

PS. They've given a really easy angular velocity.
 
  • #6
i got π radians.
So, displacement of point P would be 2r=1.25 m
 
  • #7
086qjac.png
 
  • #8
  • #9
I think you're forgetting that as P rotates round the sphere, the whole sphere is moving down.
If the sphere were not rotating, P would move the same distance as C (1:1), but the rotation adds to the displacement of P.
 
  • #10
Okay.
So answer would be 2:1.
 
  • #11

Related to Falling rotating sphere and displacements

1. What causes a rotating sphere to fall?

A rotating sphere falls due to the force of gravity acting on it. As the sphere falls, it is subject to a downward acceleration that increases its speed until it reaches the ground.

2. How is displacement calculated for a falling rotating sphere?

The displacement of a falling rotating sphere can be calculated by taking into account its initial velocity, acceleration due to gravity, and time. The formula for displacement is s = ut + 1/2at^2, where s is displacement, u is initial velocity, a is acceleration, and t is time.

3. What factors affect the displacement of a falling rotating sphere?

The displacement of a falling rotating sphere is affected by its initial velocity, the angle at which it is thrown, the acceleration due to gravity, and the time for which it falls. Other factors such as air resistance and the shape of the sphere may also play a role in the displacement.

4. Can a rotating sphere fall without displacing?

No, a rotating sphere cannot fall without displacing. Displacement is defined as the change in position of an object. Even if the sphere is rotating, it is still moving from its initial position and therefore has a displacement.

5. How does the mass of a rotating sphere affect its displacement?

The mass of a rotating sphere does not directly affect its displacement. However, a heavier sphere may experience a greater force of gravity and therefore may fall faster, resulting in a larger displacement. The displacement also depends on the initial velocity and angle at which the sphere is thrown.

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