1) A disk is initially rotating with an angular velocity of 32.0 rad/s î. The di

Question

1) A disk is initially rotating with an angular velocity of 32.0 rad/s î. The disk experiences an angular acceleration of -6.40 rad/s2 î for 20.0 seconds.

What is the angular velocity of the disk at the end of the 20.0 seconds?

What is the angular displacement of the disk during the 20.0 seconds?

What is the angular displacement of the disk during the first 7.00 seconds?

2) The angular position of an object is given by the equation:

theta(t)=(24.0 rad/s)t i -(8.50rad/s^2)t^2 i-(3.60 rad/s^3)t^3 i

a. What is the object’s angular position at t = 2.15 s?

b. What is the average angular velocity of the object between t = 1.40 s and t = 2.15 s?

c. What is the object’s instantaneous velocity at t = 1.90 s?

d. What is the average angular acceleration of the object between t = 1.25 s and t = 1.90 s?

e. What is the object’s instantaneous acceleration at t = 1.40 s?

Explanation / Answer

Ans:- 1]

W = w0 +t

     = 32 – 6.40*20

W =-96rad /s i

= w0*t + ½**t

   = 32*20 – ½*6.40 *20

= 576rad

= 32 *7 -1/2*6.40*7 = 201.6rad

2] (t)=(24.0 rad/s)t i -(8.50rad/s^2)t^2 i-(3.60 rad/s^3)t^3 i

a.(2.15) = 24*2.15i-8.50*(2.15)^2i-3.60*(2.15)^3i

                = 51.6i – 39.29i-35.78i

(2.15) = -23.47i rad

b. (1.40)=6.06irad

w = (2.15)-(1.40)/(2.15-1.40) = -29.53/0.75= -39.37irad/s

C.(1.90) =-9.78rad

W = -9.78/1.90= -5.15irad/s

D.(1.25) = 9.69rad

W = 7.75irad/s

= -5.15-7.75/0.65 = -19.85irad/s^2

e. (1.40)=6.06irad

w= 4.33rad/s

=3.09rad/s^2

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