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Can someone help me with this physics problem?
A ring with mass m and radius r has a small weight attached also with mass m. The ring can roll over a horizontal table. It is oriented in such a way that the angle between the weight and the vertical is α = π/3 radians.
a. What should the coefficient of friction f between table and ring be for it to start rolling without slipping from the given position?
b. Assuming f satisfies the above conditions, what is the angular acceleration of the ring when it starts moving?
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>>327941
a.
torque = r*mg*sin(α ) - r*N*u = (2mr^2)*angular acceleration
angular acceleration = g*sin(α)/2r - rNu/(2mr^2) = g*sin(α)/2r - 2rmgu/(2mr^2) = g*sin(α)/2r - gu/r
angular acceleration * r = linear acceleration
m*angular acceleration * r = m * linear acceleration = N*u = 2mg*u
g*sin(α)/2 - gu = 2g*u
g*sin(α)/2 = 3g*u
u = sin(α)/6
b.
angular acceleration = g*sin(α)/2r - gu/r
angular acceleration = g*sin(α)/2r - gsin(α)/6r = g*sin(α)/3r
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