I can\'t seem to get the correct answers to thefollowing problems, and was hopin

Question

I can't seem to get the correct answers to thefollowing problems, and was hoping you might point out what I'vebeen doing wrong:

I.

A constant torque of 15M*N is applied to the rim of a 8.0-kguniform disk of radius 0.30m

What is the angular speed of the disk about an axis through itscenter after it rotates 2.0 revolutions from rest?

Knowing:
torque=15mN
m= 8.0kg
r= .30m
alpha = 2(2pi)
w_0= 0
      
Using:
        w^2=w_o^2+2...
        w = squareroot of2ang_acc(alpha
        I= 1/2mr^2
        ang_acc = torque/I =2r/mr^2

so...
        w= square root of(16pi^2*torque)/mr^2

Calculated Answer: 51.30

II.


Two masses are suspended from a pulley as shown in the figure . Thepulley itself has a mass of 0.40kg, a radius of 0.25m, and aconstant torque of 0.20 mN due to the friction between the rotatingpulley and its axle.

Knowing:
M_pulley= .40kg
m1= .40kg
m2= .90kg
T_f= .20mN
r= .25m
a=?

Using:
      
        a= (m1-m2)g-T_f)/(MR/2+m2-m1)

Calculated Answer: -2.1m/s^2

Explanation / Answer

A hoop starts from rest at a height 3.0 above the base of aninclined plane and rolls down under the influence of gravity. What is the linear speed of the hoop's center of mass just as thehoop leaves the incline and rolls onto a horizontal surface?(Neglect friction.) Using: v = (2 g h) Calculated Answer: 7.6 m/s None of these answers were correct! :( Would greatly appreciate itif someone could point out my mistakes!

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