How does tension affect the motion of a hanging block on a rotating disk?

AI Thread Summary
Tension in the cord affects the motion of a hanging block on a rotating disk by influencing the net force and torque acting on the system. The equation T - mg = ma illustrates the relationship between tension, gravitational force, and acceleration. Torque is calculated using the formula torque = I α, where I represents the moment of inertia and α is the angular acceleration. The confusion arises from the sign convention used for torque; since the positive direction is defined as upward, the tension force is considered negative when calculating torque. Understanding these concepts is crucial for solving problems related to the dynamics of rotating systems.
Brandan
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Homework Statement


This figure shows a uniform disk, with mass M = 2.5 kg
and radius R = 20 cm, mounted on a fixed horizontal axle.
A block with mass m = 1.2 kg hangs from a massless cord
that is wrapped around the rim of the disk.

Sample problem 10-8 (has picture diagram and detailed solution): http://astro1.panet.utoledo.edu/~mheben/PHYS_2130/Chapter11-1_mh.pdf

Homework Equations


T – mg = ma
torque = I α
-RT ? = (1/2)MR^2 α
a = a(subscript t) = α R

The Attempt at a Solution


I understand how to do the problem but what I don't understand is how they got -RT. Torque is FrSin(theta) and the sin of 90 degrees is 1 not -1 so I would really appreciate any insight on how they got -RT.
 
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Well, it looks like positive direction is chosen to be up and vector T is pointing down so...
 
lep11 said:
Well, it looks like positive direction is chosen to be up and vector T is pointing down so...
Ok thanks
 

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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