Disk on a Motion: Find the Coordinates of Point A at t= 4piR/v

[BBAI BBAI]

Homework Statement

Adisk of radius R centred at the origin is placed on a frictionless x-y plane with origin as the centre of the disk.At t=0, the disk is given initial motion such that the point A(R,0) has velocity v towards
+ve x-axis and ω=v/2R. Find the coordinates of Point A at t= 4piR/v

Homework Equations

∅=ωt..That's all i think is needed

The Attempt at a Solution

i used but i am getting a wrong answer help!

 

[mfb]

Can you express the motion of A as functtion of the velocity of the center and ω?
Based on that, can you calculate this velocity and ω?

 

[BBAI BBAI]

That's the problem..The velocity of A at t=0 is given..How can i relate to the centre of mass velocity..

 

[mfb]

I proposed to start with the other direction (use w,ω for the center and calculate the motion of A as function of those variables) for a good reason - it is easier.
Did you try to calculate it?

 

[Nickie]

As a scientist, my response to this content would be as follows:

The problem statement describes a disk of radius R that is initially moving with a velocity v towards the positive x-axis, with an angular velocity ω=v/2R. The goal is to find the coordinates of Point A, located at (R,0), at a specific time t= 4piR/v.

To solve this problem, we can use the equation ∅=ωt, where ∅ is the angular displacement and t is the time. We know that at t=0, the disk is at its starting position and therefore, the angular displacement is also 0. We can then set up the following equation:

0=ωt= (v/2R)t

Solving for t, we get t=0. This means that at t= 4piR/v, the disk will have completed 4piR/v radians of rotation. To find the coordinates of Point A at this time, we can use basic trigonometry. The x-coordinate of Point A will be R*cos(4piR/v) and the y-coordinate will be R*sin(4piR/v). Therefore, the coordinates of Point A at t= 4piR/v are (R*cos(4piR/v), R*sin(4piR/v)).

It is important to double-check our answer to ensure it makes sense. We can see that at t=0, the disk is at its starting position and therefore, Point A is at (R,0). As time passes, the disk rotates counterclockwise and Point A will move along the circumference of the disk. At t= 4piR/v, the disk will have completed one full rotation (2pi radians) plus an additional 2piR/v radians. This means that Point A will have moved to the point directly opposite its starting position, which matches our solution.

In conclusion, the coordinates of Point A at t= 4piR/v are (R*cos(4piR/v), R*sin(4piR/v)). It is important to carefully analyze the given information and use appropriate equations to solve the problem. If you are getting a wrong answer, double-check your calculations and make sure you are using the correct equations and units.