Calculating Angular Acceleration for a Rotating Compact Disc

In summary, the problem in the physics class at Portland Community College involved finding the angular acceleration of a compact disc (CD) as it accelerated from rest to a constant rotational speed of 477 rev/min, while rotating through an angular displacement of 0.250 rev. The correct answer was option (e), 794 rad/s2, which was found by first converting the given data to SI units and then using the formula ω^2 = ω(initial)^2 + 2∂θ to solve for the angular acceleration (∂).
  • #1
gcombina
157
3
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" ****
 
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  • #2
Hi, gcombina.

Watch the units.

Note the units in your answer compared to the units in the choices of answer.
 
Last edited:
  • #3
so 477 rev/min = 477 rad/60 s? meaning 7.095 rad/s??
 
  • #4
gcombina said:
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.
 
  • #5
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!
 
  • #6
Good work!
 

Related to Calculating Angular Acceleration for a Rotating Compact Disc

1. What is angular acceleration?

Angular acceleration is the rate of change of angular velocity over time. It is a measure of how quickly an object's rotational speed is changing.

2. How is angular acceleration different from linear acceleration?

Angular acceleration is a measure of rotational motion, while linear acceleration is a measure of straight-line motion. Angular acceleration is also measured in radians per second squared, while linear acceleration is measured in meters per second squared.

3. What causes angular acceleration?

Angular acceleration can be caused by a number of factors, including a torque or force acting on an object, changes in the distribution of mass, or changes in the moment of inertia of an object.

4. How do you calculate angular acceleration?

Angular acceleration can be calculated by dividing the change in angular velocity by the change in time. This can be represented by the equation α = Δω/Δt, where α is angular acceleration, Δω is the change in angular velocity, and Δt is the change in time.

5. What is the relationship between angular acceleration and angular velocity?

Angular acceleration and angular velocity are directly related, as angular acceleration is the rate of change of angular velocity. This means that as angular acceleration increases, so does angular velocity, and vice versa.

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