Calculating Angular Acceleration for a Rotating Compact Disc

[gcombina]

Problem(physics class 201/Portland Community College)
During the time a compact disc (CD) accelerates from rest to a constant rotational speed of 477 rev/min, it rotates through an angular displacement of 0.250 rev. What is the angular acceleration of the CD?
(a) 358 rad/s2 (c) 901 rad/s2 (e) 794 rad/s2
(b) 126 rad/s2 (d) 866 rad/s2


This is my formula from my Kinetics formula in my book where ∂ = angular acceleration

(1)Kinetics formula
V^2 = V(initial)^2 + 2ax

(2)so I converted to:
ω^2 = ω(initial)^2 + 2∂θ
(477 rev/mins)^2 = (0 rad/s)^2 + 2(∂)(0.250 rev)
[(477 rev/mins)^2 - (0 rad/s)^2)]/ (2 (0.250 rev))= ∂
[(477 rev/mins)^2 - 0] / (.50 rev) = ∂
(477 rev/mins)^2 / .50 rev = ∂
(227529 rev^2/mins^2) / .50 rev = ∂
455,058 rev/mins^2 = ∂

**** I can not get the answer! the Answer is "e" ****

 

[TSny]

Hi, gcombina.

Watch the units.

Note the units in your answer compared to the units in the choices of answer.

 

[gcombina]

so 477 rev/min = 477 rad/60 s? meaning 7.095 rad/s??

 

[TSny]

so 477 rev/min = 477 rad/60 s? meaning 7.095 rad/s??

How many radians in a revolution?

Note: I believe your original answer is correct in rev/min². So, you could just convert it to rad/s². However, I think it would be worthwhile for you to also work the problem by first converting the given data to SI units.

 

[gcombina]

I got it!
thanks!
ω^2 = ω(initial)^2 + 2∂θ

converted
477 rev/min into rad/s ===> converted to 477 (2pi)rad/60s) because 1 revolution equals a 2pi radian
0.25 rev ====> converted to 1.57 because 1rev = 2pi therefore, 0.25 (2pi) = 0.25 (2(3.1415)) = 1.57a

after converting the revolutions to radians, I just plug in the numbers
(49.95 rad/s )^2 = (0 rad/s)^2 + 2(α)(1.57)
[(2495 rad/s) - (0 rad/s)^2] = 2 (α) (1.57)
2495 rad/s = 3.14 (α)
(2495 rad/s) / (3.14) = α
α = 795

))) thanks!

 

[TSny]

Good work!