Id like to see step by step please so I can know what exactly needs to be done T

Question

Id like to see step by step please so I can know what exactly needs to be done

The disk shown above has radius 2,50m and mass of 10.0kg. It has an angular velocity of 9.50 rad/s at t = 0s about its center 0, moving in the CounterClockwise direction. It also experiences a Clockwise angular acceleration of 1.00 rad/s^2. a) What is the disk's moment of inertia? b) What Kinetic Energy does the disk possess at t=0.00s and at t=6.00s? c) How long does it take for the disk to stop rotating momentarily? d) What is the disks' angular displacement after 6.00s? e) What is the disks' angular speed when it reaches an angular displacement of -10.3 rad?

Explanation / Answer

a) for disk, I = 0.5*M*R^2

= 0.5*10*2.5^2

= 31.25 kg.m^2

b) at t = 0, wo = 10 rad/s

KE = 0.5*I*wo^2

= 0.5*31.25*9.5^2

= 1410.16 J

at t = 6s, alfa = -1 rad/s^2

w = wo + lfa*t

= 9.5 - 1*6

= 3.5 rad/s

KE = 0.5*I*w^2

= 0.5*31.25*3.5^2

= 191.4 J

c)

w = wo + alfa*t

0 = 9.5 - 1*t

==> t = 9.5 s

d)

theta = wo*t + 05*alfa*t^2

= 9.5*9.5 - 0.5*1*9.5^2

= 45.125 rad

e)

w^2 - wo^2 = 2*alfa*theta

w^2 = wo^2 + 2*alfa*theta

= 9.5^2 + 2*1*10.3

= 110.85

w = 10.53 rad/s

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