Imagine in my upcoming AP Physics exam I had to use this formula: w=2πf. But in stead, I flipped the formula and used w=2π/f by mistake...?
How much will I be penalized in that question's part and the parts after it?
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Totally zero. What you have is total gibberish with rad/s as units on the LHS and sec/cycle on the RHS. In fact you've said that angular speed is equal to period. You might as well have said that apples equal oranges. Zero.
The answers will be wrong; you will get 0 for it
Difficult to say without knowing the marking scheme. Check the marking scheme for the Exam Board and you should be able to figure it out.