What Are Those Circular Driveways in Front of Mansions Called?

You can not expect someone to clean up a dead animal from the road. If it bothered you so much, you could do it yourself. Personally, I would not touch a dead animal. Between possible disease and possibly getting hit by a car myself, I would leave the poor squirrel be. I do not think it minds

What Are Those Circular Driveways in Front of Mansions Called? 1

1. What is the best circular knitting device in your opinion?

I agree with Aussie Sheila to a degree as there are alternatives (a regular home knitting machine with ribber will knit circular knitting beautifully), however if you absolutely HAVE to have one of these, and can not afford something like a sock machine, then the Addi Express seems to get the most positive reviews

2. What are the differences between circular reasoning and proof by definition?

Circular reasoning, sometimes referred to ad "begging the question" means using the conclusion as part of the proof. It's obviously invalid.Proof by definition is a less formally defined idea, meaning that a conclusion follows directly or with little deduction from the definition of a term. "0/0 is not a real number" follows almost immediately from the definition of division in the real number system. Proof by definition is absolutely valid.

What Are Those Circular Driveways in Front of Mansions Called? 2

3. Difference between circular motion and rotational motion

The main difference between these types of motion is that circular motion is a special case of rotational motion, where the distance between the body's centre of mass and the axis of rotation remains fixed.Rotational motion is based around the idea of rotation of a body about its center of mass. In rotational motion, the axis of rotation and centre of mass could change whereas in circular motion, the axis of rotation and centre of mass does not change. Circular motion is a movement of an object along the circumference of a circle or rotation along a circular path and can either have a constant angular rotation rate and constant speed, or it can exist with a changing rate of rotation.Think of one of those fairground rides where people sit on dummy horses. Now imagine the horses spin around the post that holds them to the base of the ride. Then you have both rotational motion of the horse and circular motion as the horses move around the ride.I think you may have this the wrong way round.Have a read of this link: Circular Versus Rotational Motion.

4. Ball rolling down circular incline

As you noted at the end in doing the integration to obtain $v-v_0=mgsin(theta)t$ you have assumed that $sin(theta)$ is constant which it is not.The analysis is easier if the ball does not roll and the frictional force is zero. The tangential force at any time $t$ is your $mgsin(theta)$.Also the linear speed $v$ is connected to the rate of change of angle $omega =fracdthetadt=dot theta$ $v=(Rr)omega$ where $R$ is the radius of the track and $r$ is the radius of the ball. So the linear acceleration $a=fracdv dt = (Rr) dot omega = (Rr) ddot theta approx R ddot theta$ if $R>>r$So you have to solve $gsin theta=R ddot theta$. Multiply both sides by the linear speed $v=Rdot theta$$v R ddot theta = v dfracdvdt$ and $vg sin theta = gR sin theta dfrac dthetadt$and integrate$displaystyle int ^v _0 v ; dv= gR int ^theta _0 sin theta ; d theta Rightarrow dfrac 12 v^2 = gr (1 -cos theta)$which is a long-winded way of applying conservation of energy directly.Gain in kinetic energy = loss in potential energy $Rightarrow dfrac 12 mv^2 = mgr (1 -cos theta)$To find the angle $theta$ as a function of time ie solve $gsin theta=R ddot theta$ for $theta(t)$ is much more difficult and WolframAlpha with the input of solve[theta''[t]=sin( theta[t])] tells me it requires the Jacobi amplitude function. So you now have $mgsin theta - F=mR ddot theta$ and $Fr = I_

m c ddot phi$ where $ddot phi$ is the angular acceleration of the ball, $r$ is the radius of the ball and $I_

m c$ is the moment of inertial of the ball about its centre of mass.$Rddot theta = r ddot phi Rightarrow F= dfracI_

m cR ddot thetar^2 $Substituting for $F$ gives $mgsin theta = left (mdfrac I_

m c r^2

ight ) R ddot theta$ with the bracket having an extra term from the equation when it was assumed that the ball was not spinning $dfrac I_

m c r^2 $ which is the extra inertia due to the ball spinning.

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