If you both have shared 50/50 custody and physical custody and there was no child support ordered then unless she files a motion for child support you do not have to pay any support at this time.
just because the mother is not working does not mean she can't go to work,she is responiable for taking care of her child when the child is with her like you have to when the child is with you. The court is not going to just grant her child support,you might want to consider filing for soleand give custody giving her visitations,since you have a job and home for the child verses she is not working and has only one BR.

But that is your child giving some money or items for your child would help because you still are responsible for that child lieke clothes and bathing items maybe toyus and such you are the father regardless of court orders speaking from a mothers stand point i do not get anything from his father but clothes and toys would have helped if he didnt want to give me money

In court here are a few things the judge will put into consideration depending on what custody guidelines your state has.
-wishes of the child if old enough
-mental & physical health of parents
-religion/cultural considerations
-need for continuation of stable home environment
-support & opportunity for interaction with members of extended family of either parent
-interaction & interrelationship with other members of household
-adjustment to school & community
-age & sex of the child
-parental use of excessive discipline or emotional abuse
-evidence of parental drug, alcohol or sex abuse
-health of child
-parenting skills of each parent
-parent that has the willingness & capacity to provide primary childcare
-employment of each parent & the responsiblities of that employment
-emotional ties between parent & child
-& other factors relevant each judge is different

Child support is based on income earned. Usually in a 50/50 custody situation, unless you are making equal incomes, child support is based on the difference of income between the two of you. For example if you made 50,000 and she made 30,000, child support would be set to offset that disparity between your incomes. The goal would be to move both households to the income of 40,000 to equal out the difference.

However, if you provide the health insurance for the child and that costs you 4000 per year, that comes out of 10,000 you would be expected to pay annually because of the difference in your incomes. This would leave you owing 6000 in child support over the coarse of a year which breaks down to roughly 500.00 per month. Day care costs are also taken into consideration.

Child support and the way that it is determined varies from state to state, however most states use what is known as income shares model which I explained above. You can find information on line regarding how your state determines child support. You can also access child support worksheets on line to help you better figure out how your state will view your situation.

It is true that both parents are expected to support the child. Being that your ex is not working and sounds as if she does not have reasonable accommodations for the child, you may want to speak to an attorney about your chances of getting sole custody. Child support applies to men and women equally and if you were able to get sole custody, your ex would be responsible for paying child support to you. However, it is not easy to get sole custody.

However, you always have to consider what is in the best interest of your child and the courts will consider this above all other considerations. I think the best case scenario would be for you to pursue joint legal and physical custody where you are the primary parent. This would mean that you have the child most of the time and your ex might have the child every other weekend. It is much easier to try and get joint legal physical custody as opposed to sole custody. In this scenario, your ex would still be liable for paying child support to you.