Hi, My name is XXXXX XXXXX I’m happy to assist you with your question today.
There are really two questions here. First question is - may an employer that only offers limited work (part time) require you to available any workday of the week. The answer to that is yes they can require you to available to work any day of the week as a condition of employment. It is between you and them if that is an agreeable arrangement.
The second question is whether they need to compensate you extra for this. The Fair Labor Standards is the law that is applicable to this (the FLSA). The FLSA essentially states that you are to be compensated for on call time if you cannot effectively use that time for your own use. "An employee
who is required to remain on call on the employer's premises or so close thereto that he cannot use the time effectively for his own purposes is working while “on call”. An employee who is not required to remain on the employer's premises but is merely required to leave word at his home or with company officials where he may be reached is not working while on call. ( Armour & Co. v. Wantock, 323 U.S. 126 (1944); Handler v. Thrasher, 191 F. 2d 120 (C.A. 10, 1951); Walling v. Bank of Waynesboro, Georgia, 61 F. Supp. 384 (S.D. Ga. 1945))".
Being "on-call" is distinguishable from just being available. If they just are saying, for example, week one we can schedule you Mon-Wed, and Week two Wed-Fri...and you have to be available for that, then that is not compensable; you'd have to negotiate extra pay for that if you believe it is a hindrance to your time. But if they're saying we can call you any time on a moments notice and you have to be to work in 5 minutes then that is compensable because you effectively cannot use that time for your own purposes. A slight nuance that makes a big difference.
I believe this answers your question. However, if you need clarification or have follow-up questions regarding this matter, I will be happy to continue our conversation – simply reply to this answer. If you are otherwise satisfied with my response, please leave a positive rating as it is the only way I am able to get credit for my answers. Thank you, XXXXX XXXXX wish you all the best with this matter.