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Sakura91
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Homework Statement
An object is placed on a turntable with a radius of 21.5 cm. The object's mass is 67.5 g. The coefficient of static friction between the two is .32. It asks to find the maximum angular velocity the object can have while remaining stationary relative to the turntable in radians per second.
The second part says that the turntable starts from rest at t = 0, and it has a constant angular acceleration of 3.82 rad/s^2. It asks at what time will the object begin to slip.
Please help!
Homework Equations
Force of static friction = m*g*mu_static
Centripetal, or radial, acceleration = v^2/r
v = sqrt(r*g*mu_static)
The Attempt at a Solution
The idea is that up to a certain velocity, the static friction force should prevent the object from moving outside of the circular trajectory. So, I set v^2/r <= g*mu_static, and solved for v, which is about .82112 m/s. The reason why I went with radial acceleration was because I know that the overall centripetal acceleration will combat against friction's acceleration and force, and I know that the magnitude of that acceleration is sqrt(a_radial^2 + a_tangential^2). I'm having a hard time establishing relationships because it's hard for me to visualize what is affecting what.