# Answer to Question #166084 in Mechanical Engineering for Yashwanth

Question #166084

A small 250g collar C can slide on a semicircular rod which is made to rotate about the vertical AB at a constant rate of 7.5rad/s. Determine the 3 values of theta for which the collar will not slide on the rod, assuming no friction b/w the collar and the rod.

1
2021-02-25T04:15:09-0500 We can assume r= 950 as we have not been provided.

"R=rsin\\theta=950sin\\theta; v=Rw"

"a_0=\\frac{v^2}{R}=\\frac{R^2w^2}{R}=rsin\\theta w^2"

"\\sum{Fy}=ma_y \\implies Ncos \\theta-mg=0 \\implies N=\\frac{mg}{cos\\theta}"

"\\sum{Fx}=ma_x \\implies Nsin \\theta-ma=0 \\implies sin \\theta=\\frac{ma}{N}"

"rsin\\theta cos\\theta w^2-gsin\\theta=0"

"So, cos \\theta = \\frac{g}{rw^2} or \\space sin\\theta=0"

"cos\\theta=\\frac{9.8}{0.95*7.5^2} \\implies \\theta=79.42^0"

"sin\\theta=0 \\implies \\theta =0^0 or 180^0"

Need a fast expert's response?

Submit order

and get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!