Non-urgent question; nothing to do with GCSEs; it's about direction and acceleration.
Say I force a cat to move in a circle of radius 10 m clockwise; let's say it takes 11 seconds for the cat to go around the circle for the first time, 12 seconds for the second time, 13 seconds for the third time and so on, and the cat completes 20 laps of the circle until it becomes exhausted and I let it take a rest. Since moving in a circle means the direction always changes, is the cat constantly 'accelerating' even when the speed is decreasing? If so, how do you work out the acceleration/deceleration (in terms of both change in speed and direction), or is it even possible to do so?
Original post by flibber
Say I force a cat to move in a circle of radius 10 m clockwise; the cat completes 20 laps of the circle until it becomes exhausted
You monster!
In a situation in which something is moving around in a circle with the same period, there is a centripetal acceleration - this is constant. The cat changes direction but not its tangential velocity at any point.
If, like in your model, the period is increasing, it means there is a centripetal acceleration which, this time, is continually decreasing. This again causes continual changing in direction but - with constant radius - causes the cat's tangential velocity at any point to be decreasing also.
You have to understand the distinction between the centripetal acceleration affecting the angular velocity and also the tangential (linear) velocity at any point. It's all to do with frames of reference.
(edited 9 years ago)
Original post by sjgriffiths
You monster!
In a situation in which something is moving around in a circle with the same period, there is a centripetal acceleration - this is constant. The cat changes direction but not its tangential velocity at any point.
If, like in your model, the period is increasing, it means there is a centripetal acceleration which, this time, is continually decreasing. This again causes continual changing in direction but - with constant radius - causes the cat's tangential velocity at any point to be decreasing also.
You have to understand the distinction between the centripetal acceleration affecting the angular velocity and also the tangential (linear) velocity at any point. It's all to do with frames of reference.
In a situation in which something is moving around in a circle with the same period, there is a centripetal acceleration - this is constant. The cat changes direction but not its tangential velocity at any point.
If, like in your model, the period is increasing, it means there is a centripetal acceleration which, this time, is continually decreasing. This again causes continual changing in direction but - with constant radius - causes the cat's tangential velocity at any point to be decreasing also.
You have to understand the distinction between the centripetal acceleration affecting the angular velocity and also the tangential (linear) velocity at any point. It's all to do with frames of reference.
The equation for centripetal acceleration, mv2/r (for the purposes of this question, I shall assume that the mass of the cat is 70 kg; it was supposed to have been put down for stealing other cats' food in the animal shelter, but then I kidnapped it for my own sadistic purposes) was explicitly stated in the AQA GCSE Specification as not being needed for my exams. But that's irrelevant given that the whole question has nothing to do with my exams.
I shall see if I can look up the relevant stuff required myself and solve the question.
Is this covered in A Level Physics, or in any of the Maths Mechanics modules?
(edited 9 years ago)
Original post by flibber
The equation for centripetal acceleration, mv2/r (for the purposes of this question, I shall assume that the mass of the cat is 70 kg; it was supposed to have been put down for stealing other cats' food in the animal shelter, but then I kidnapped it for my own sadistic purposes) was explicitly stated in the AQA GCSE Specification as not being needed for my exams. But that's irrelevant given that the whole question has nothing to do with my exams.
I shall see if I can look up the relevant stuff required myself and solve the question.
Is this covered in A Level Physics, or in any of the Maths Mechanics modules?
I shall see if I can look up the relevant stuff required myself and solve the question.
Is this covered in A Level Physics, or in any of the Maths Mechanics modules?
mv2/r actually gives the centripetal force, which is of course related to the centripetal acceleration via Newton's F=ma.
Circular motion was definitely not needed for GCSE, but, yes, it gets covered in the further mechanics section of A2 Physics (also linking in to the gravitational, electric and magnetic fields work in that same course). I'm also studying maths M1 and M2 but as far as I'm aware circular motion makes an appearance in neither of these. Perhaps it will in later mechanics modules, but it does definitely appear in A2 physics.
Original post by flibber
The equation for centripetal acceleration, mv2/r (for the purposes of this question, I shall assume that the mass of the cat is 70 kg; it was supposed to have been put down for stealing other cats' food in the animal shelter, but then I kidnapped it for my own sadistic purposes) was explicitly stated in the AQA GCSE Specification as not being needed for my exams. But that's irrelevant given that the whole question has nothing to do with my exams.
I shall see if I can look up the relevant stuff required myself and solve the question.
Is this covered in A Level Physics, or in any of the Maths Mechanics modules?
I shall see if I can look up the relevant stuff required myself and solve the question.
Is this covered in A Level Physics, or in any of the Maths Mechanics modules?
Seeing as your cat is slowing down, I doubt you can use a=v^2/r as that's derived on the understanding of a constant velocity.
Acceleration simply means a change in velocity over time- the best way to think about it for this would probably be to consider individual components. You can break up vectors into different 'components' which are at right angles, so a typical velocity vector might look like:
(5i+7j-2k)ms-2 (where i,j and k are called 'unit vectors' and basically just indicate the x,y and z directions.)
To find an acceleration you do difference in velocity over difference in time. You do this for each component separately, then add them together again- hence why changing direction counts as acceleration, because changing direction changes the mix of i,j and k so when you do the subtraction you get a non-zero answer.
Long story short: unless you're velocity remains the same in each direction, you must be accelerating.
(edited 9 years ago)
Original post by flibber
Say I force a cat to move in a circle of radius 10 m clockwise; let's say it takes 11 seconds for the cat to go around the circle for the first time, 12 seconds for the second time, 13 seconds for the third time and so on, and the cat completes 20 laps of the circle until it becomes exhausted and I let it take a rest. Since moving in a circle means the direction always changes, is the cat constantly 'accelerating' even when the speed is decreasing? If so, how do you work out the acceleration/deceleration (in terms of both change in speed and direction), or is it even possible to do so?
The resultant acceleration of the cat at any point will be the vector sum of
- its centripetal acceleration v2/r
- and its tangential (linear) acceleration calculated from the usual change in velocity divided by time taken.
The two are at right angles giving a resultant which is not now directed towards the centre.
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