Rotational Kinematics/Tension Problem

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To solve the problem of a cylinder on an inclined plane with a tension force, the tension T required for equilibrium can be determined using the equations of motion and rotational dynamics. The relationship between tension, gravitational force, and friction must be analyzed to find T. If the tension differs from T, the acceleration of the cylinder can be calculated by applying Newton's second law and considering the torque produced by the tension. The problem emphasizes the importance of providing a complete attempt at the solution to facilitate assistance. Understanding the balance of forces and torques is crucial for solving both parts of the problem effectively.
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Homework Statement


A cylinder of known mass M, radius R, and rotational inertia I is placed on an inclined plane with angle θ. A string is wound around the cylinder and pulled up with a tension T parallel to the inclined plane. The coefficient of static friction is large enough to prevent slipping.

a) Find the tension T needed to keep the cylinder in equilibrium
b) Find the acceleration of the cylinder if the tension is known and is different from T.

Homework Equations

The Attempt at a Solution

 
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Thread 'Errors and significant figures'

I multiplied the values first without the error limit. Got 19.38. rounded it off to 2 significant figures since the given data has 2 significant figures. So = 19. For error I used the above formula. It comes out about 1.48. Now my question is. Should I write the answer as 19±1.5 (rounding 1.48 to 2 significant figures) OR should I write it as 19±1. So in short, should the error have same number of significant figures as the mean value or should it have the same number of decimal places as...
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Thread 'A cylinder connected to a hanging mass'

Thread 'A cylinder connected to a hanging mass'

Let's declare that for the cylinder, mass = M = 10 kg Radius = R = 4 m For the wall and the floor, Friction coeff = ##\mu## = 0.5 For the hanging mass, mass = m = 11 kg First, we divide the force according to their respective plane (x and y thing, correct me if I'm wrong) and according to which, cylinder or the hanging mass, they're working on. Force on the hanging mass $$mg - T = ma$$ Force(Cylinder) on y $$N_f + f_w - Mg = 0$$ Force(Cylinder) on x $$T + f_f - N_w = Ma$$ There's also...
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