please help. have a test in under 12 hours and this one question is 25% of the t

Question

please help. have a test in under 12 hours and this one question is 25% of the test.

Q- A horizontal uniform solid disk of mass 3 kg and radius 2 m starts from rest and rotates, about a vertical axis through its center, with a constant angular acceleration. At 0.5 s, it is rotating with an angular speed of 4 rad/s

1)Through what angle has the disk turned during the first 0.5 s?

2)What is the angular acceleration of the disk?

3)How fast is a point on the rim moving at 0.5 s?

4)What is the angular momentum of the disk at 0.5 s?

5)What torque is being applied to the disk?

Explanation / Answer

angular acceleration( ) = / t = 4rad/s / 0.5s = 8 rad/s^2

   is angular velocity

t is time

1 applying laws of motion.

angle turned (theta )= 0.5 * *t^2 = 0.5*8*0.5^2 = 1.0 rad (= 57.3 o)

2.)  angular acceleration( ) = / t = 4rad/s / 0.5s = 8 rad/s^2

3) velocity( v ) = r * = 2m * 4rad/s = 8 m/s

r is radius of disk

4. Moment of Inertia of solid disk I = 0.5*m*r^2 = 0.5*3kg*(2m)^2 = 6 kg.m^2

Angular momentum = I * = 6kg.m^2 * 4rad/s = 24 kg.m^2/s

5. Torque T = I * = 6 * 8 N.m = 48 N.m

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