Rate of forward motion from rolling rectangle vs degrees turned

In summary, Tiny-Tim's problem is that he needs to find the coordinates of the centre of a rolling rectangle as it moves along a circle with a radius drawn from the centre to the corner.
  • #36
brimby said:
… What I really need is the relationship between Δθ and Δcosθ, so I can say "(cosThetaVelocity (Δcosθ)) = (rotationalVelocity (Δθ) altered by some constant), or put another way, "as the angle of θ changes, the value cosθ changes by some amount."

no such formula exists …

Δcosθ/Δθ changes (it depends on θ)
… Maybe I should just turn the whole thing around and have the Δcos/Δsin values directly affected by the player's actions rather than Δθ. That would put it more in the direction I'm used to working. I'm still interested in what you have to say about how I framed it first though, because for all I know at this point, doing it that way would reverse some other thing that would screw me over.

i don't understand what the player would be doing :confused:

wouldn't he normally either want to push the box a given distance, or hit it with a given force?

why would he want to specify an angle?
 
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  • #37
You know what, scratch that whole last ramble. I've decided that switching the directly affected values to Δcos and Δsin is definitely the way to go. It doesn't make sense that the character hits the rectangle and its degrees of rotation is what is directly affected. The forward motion of the attack doesn't translate into rotation, the amount it moves up and forward is what is actually being directly affected. It's going to add a whole 'nother layer to the physics where I have to calculate at what point the object lifts off the ground rather than keeps it's corner planted and rotates, but I want that level of richness to the physics, no matter how long it takes me to work through it. ;)
 
  • #38
tiny-tim said:
why would he want to specify an angle?

Yeah, that's my problem. I was saying "the rotationVelocity (Δθ) of the object is equal to the attackVelocity of the player" but there is no reason why that would directly translate. I need to make the attackVelocity affect the x and y velocity of one side of the rectangle, and calculate the θ from that.
 
  • #39
brimby said:
Yeah, that's my problem. I was saying "the rotationVelocity (Δθ) of the object is equal to the attackVelocity of the player" but there is no reason why that would directly translate. I need to make the attackVelocity affect the x and y velocity of one side of the rectangle, and calculate the θ from that.

what is the player hitting the block with?

anyway, it looks as if you'll need to use moments of force, and moment of inertia, about the forward edge, so as to find the initial speed of rotation after each hit

(if you don't know what those are, you've a lot of reading, and worked examples, to get through)
 
  • #40
brimby said:
but I want that level of richness to the physics, no matter how long it takes me to work through it. ;)

But don't worry, once I finally get through this initial exercise, I'm going to give the rectangle (and the people of this forum) a break and work on some other stuff for a while.
 
  • #41
tiny-tim said:
(if you don't know what those are, you've a lot of reading, and worked examples, to get through)

Noted. For now I'll probably just cheat and set Δx and Δy equal to some constant.

I'll work on the block tipping properties next. I've noticed there are some good discussions already laid out on that at this forum.
 
  • #42
brimby said:
You know what, scratch that whole last ramble. I've decided that switching the directly affected values to Δcos and Δsin is definitely the way to go. It doesn't make sense that the character hits the rectangle and its degrees of rotation is what is directly affected. The forward motion of the attack doesn't translate into rotation, the amount it moves up and forward is what is actually being directly affected. It's going to add a whole 'nother layer to the physics where I have to calculate at what point the object lifts off the ground rather than keeps it's corner planted and rotates, but I want that level of richness to the physics, no matter how long it takes me to work through it. ;)

Sounds to me like you're redefining the problem. The version in the OP is no longer relevant, right?
But I'm unclear what the new definition is. (Perhaps a new thread is appropriate.)
Are you trying to model a rectangular block being hit and sent rolling and bouncing? Do you want it to obey the normal laws of physics?

Fwiw, the solution to the OP is of the form y = A(sin(φ)|cos(θ)| + cos(φ)|sin(θ)|), and x = ∫y.dθ.
 
  • #43
haruspex said:
Are you trying to model a rectangular block being hit and sent rolling and bouncing? Do you want it to obey the normal laws of physics?

Yes.
 
  • #44
In that case, your main problem is detecting and handling the bounces.
At the instant before a bounce, you have the horizontal and vertical positions, the horizontal and vertical velocities, and the rotational velocity. You need to calculate the three resulting velocities.
Do you want to take friction into account? I'll assume not, for now.
At bounce, there is an impulse normal to the surface. There will be loss of energy. You'll need to choose a coefficient of restitution.
 
<h2>1. What is the relationship between the rate of forward motion and the degrees turned of a rolling rectangle?</h2><p>The rate of forward motion of a rolling rectangle is directly proportional to the degrees turned. This means that as the number of degrees turned increases, the rate of forward motion also increases.</p><h2>2. How does the shape of the rectangle affect the rate of forward motion?</h2><p>The shape of the rectangle does not have a significant impact on the rate of forward motion. As long as the rectangle is able to roll smoothly without any friction or obstacles, the rate of forward motion will be determined by the degrees turned.</p><h2>3. Is the rate of forward motion affected by the surface the rectangle is rolling on?</h2><p>Yes, the surface the rectangle is rolling on can affect the rate of forward motion. A smooth and flat surface will allow the rectangle to roll more easily and therefore increase the rate of forward motion. A rough or uneven surface may slow down the rate of forward motion due to increased friction.</p><h2>4. Can the rate of forward motion be greater than the degrees turned?</h2><p>No, the rate of forward motion cannot be greater than the degrees turned. The rate of forward motion is determined by the number of degrees turned and cannot exceed it.</p><h2>5. How can the rate of forward motion be calculated?</h2><p>The rate of forward motion can be calculated by dividing the distance traveled by the time it took for the rectangle to travel that distance. This can be represented by the equation: rate = distance/time.</p>

1. What is the relationship between the rate of forward motion and the degrees turned of a rolling rectangle?

The rate of forward motion of a rolling rectangle is directly proportional to the degrees turned. This means that as the number of degrees turned increases, the rate of forward motion also increases.

2. How does the shape of the rectangle affect the rate of forward motion?

The shape of the rectangle does not have a significant impact on the rate of forward motion. As long as the rectangle is able to roll smoothly without any friction or obstacles, the rate of forward motion will be determined by the degrees turned.

3. Is the rate of forward motion affected by the surface the rectangle is rolling on?

Yes, the surface the rectangle is rolling on can affect the rate of forward motion. A smooth and flat surface will allow the rectangle to roll more easily and therefore increase the rate of forward motion. A rough or uneven surface may slow down the rate of forward motion due to increased friction.

4. Can the rate of forward motion be greater than the degrees turned?

No, the rate of forward motion cannot be greater than the degrees turned. The rate of forward motion is determined by the number of degrees turned and cannot exceed it.

5. How can the rate of forward motion be calculated?

The rate of forward motion can be calculated by dividing the distance traveled by the time it took for the rectangle to travel that distance. This can be represented by the equation: rate = distance/time.

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