Rotation and translation (of life importance)

[FermatPell]

A rotating disc moves in the positive direction of the x axis. Find the equation y(X) describing the position of the instantaneous axis of rotation, if at the initial moment the axis C of the disc was located at the point O after which it moved

(A) with a constant velocity v, while the disc started rotating counterclockwise with a constant angular acceleration (beta) (the initial angular velocity is equal to zero);
(B) with a constant acceleration (omega) (and the zero initial velocity), while the disc rotates counterclockwise with a constant angular velocity (omega)

I don't understand it - if the instantaneous axis of rotation always passes through the point of contact between ground and a disc, isn't it like trivial?

could some1 solve it pls?? its for my gf she will kill me if i don't solve it by the morning. (if she's reading this, go away)

 

[tiny-tim]

Welcome to PF!

Hi FermatPell! Welcome to PF!

(have a beta: β and an omega: ω )

… I don't understand it - if the instantaneous axis of rotation always passes through the point of contact between ground and a disc, isn't it like trivial?

I think the disc is flat, not rolling upright.

 

[kerimek]

I would advise against asking for someone else to solve a problem for your girlfriend. It is important for her to understand and learn the concepts herself. However, I can provide an explanation of the problem and some guidance on how to approach it.

The problem is asking for an equation that describes the position of the instantaneous axis of rotation of a rotating disc. The instantaneous axis of rotation is the imaginary line around which an object appears to rotate at any given moment. In this case, the disc is rotating counterclockwise, which means the instantaneous axis of rotation will be on the left side of the disc.

For part (A), the disc is moving in the positive direction of the x axis at a constant velocity while also rotating counterclockwise with a constant angular acceleration. This means that the disc is undergoing both translation (movement in a straight line) and rotation simultaneously. The equation for the position of the instantaneous axis of rotation in this case can be derived using the equations for linear and angular motion. It will involve the variables v (linear velocity), beta (angular acceleration), and x (position along the x axis).

For part (B), the disc is accelerating in the positive direction of the x axis while rotating counterclockwise at a constant angular velocity. The instantaneous axis of rotation will also be on the left side of the disc in this case. Again, the equation for the position of the instantaneous axis of rotation can be derived using the equations for linear and angular motion, and will involve the variables omega (angular velocity), alpha (angular acceleration), and x.

To solve these equations, you will need to use calculus and the relationships between linear and angular quantities (such as s = r*theta, where s is linear displacement, r is the radius of rotation, and theta is the angular displacement). It is important to understand the concepts of rotation and translation in order to solve these equations.

In summary, the problem is not trivial and requires a good understanding of rotational and translational motion. I would suggest reviewing these concepts and working through the equations step by step to derive the equations for the position of the instantaneous axis of rotation in both cases. Good luck!