Q1- A transverse wave on a string has the equation y(x, t) = (1.5 m)*sin((43 m-1)*x-(2577 rad/s)*t). If the tension in the string is 270 N, what is the mass per unit length?
Do we not use the formula v=w/k and plug the v into the equation v = √(Fₜ/ μ) to solve for μ for the answer? "w" being 2577 and "k" being 43. I get something like 0.075kg/m, if the method is correct could it be that I am making an error by not converting some units?
Q2 -A torque is applied to a point on the rim of a wheel. The force has instantaneous components of (0.0i + 37.6j) N and the point on the wheel has a coordinate of 0.168i m. If the wheel can be satisfactorily modeled as a uniform disk with mass 1.28 kg and radius 0.168 m, what is the magnitude of the angular acceleration of the wheel in rad/s2?
For this problem, do we not use the r and F to calculate τ, then find the moment of inertia of the uniform disk using the formula I = (1/2)(m)(r²) and use the formula τ = I x α to calculate angular acceleration? I think maybe I am making some errors with the units again. I get something like 349.70 rad/s2. Maybe I didn't convert some units somewhere.
I wanted to show what I got so it's easier to figure out if my units are the problem. The whole method I am using could be wrong though but I can't think of another way of solving these. I would appreciate any help that could guide me in the right direction.
