Does the Variable ##t## Represent Multiple Concepts in Physics Problems?

[kanekiyura]

Homework Statement

A rigid thin ring shaped like a circle of radius R rotates
uniformly around a fixed axis passing through one of the points of the circle and perpendicular to its plane. An ant crawls along the ring, moving all the time relative to the annulus with a constant velocity.At time t = 0, the velocity of the ant relative to a stationary observer is maximal and equal to v1.After time t, this velocity becomes minimal for the first time and equal to v2. Find the law of variation of the velocity value v(t).

Relevant Equations

I really don't know

I do not know how to solve this. All I got was to exclude the speed of the ant relative to the ring from the equation for its full speed

 

[BvU]

Hello @kanekiyura ,

​

Unfortunately, PF doesn't work this way. The PF guidelines dictate that you post your best attempt at solution before we are allowed to help.

Make some sketches that help you find ##v_1## and ##v_2##.

##\ ##

 

[haruspex]

First, to be accurate, it's the ant's speed that can be constant relative to the periphery of the ring, not its velocity. The velocity keeps changing direction.
Can you write an equation for the velocity of the centre of the ring at time t? And an equation for the ant's velocity relative to the centre of the ring?

 

[kuruman]

After time t, this velocity becomes minimal for the first time and equal to v2. Find the law of variation of the velocity value v(t).

Is there consensus that symbol ##t## is used rather carelessly to stand for two different entities?
1. A specific time at which the "velocity becomes minimal for the first time and equal to v2."
2. The independent variable in "the law of variation of the velocity value v(t)."

If that is the case, then perhaps a clearer formulation of the relevant section might be

At time ##t = 0##, the velocity of the ant relative to a stationary observer is maximal and equal to ##v_1.## At time ##t=t_2## this velocity becomes minimal and equal to ##v_2##. Find the law of variation of the velocity ##v(t).##