Calculating Angular Displacement of CD with Radius 6.0 cm

In summary, the angular displacement of a CD with a radius of 6.0cm and an angular velocity of 5.0 rad/s after 2.0 seconds is 10 radians, and a point on its circumference will have moved 60 cm. The radial acceleration is not needed to calculate the angular displacement.
  • #1
Anthonyphy2013
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Homework Statement



If the radius of theCD below is 6.0cm and the angular velocity is 5.0 rad/s , what's is its angular displacement in 2.0s ?

Homework Equations



Delta θ = ωt+.5∂t^2

The Attempt at a Solution


I know the angular velocity and the time but how can I find out the radial acceleration or should I use the other equation to find the angular displacement ?
 
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  • #2
The radial acceleration is irrelevant (and, in any case, 0 because the CD is not changing radius). If the CD is rotating at 5 radians per second, in two seconds it will have rotated through 5(2)= 10 radians. Since the CD has radius 6 cm, a point on its circumference will have moved 6(10)= 60 cm.
 
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Related to Calculating Angular Displacement of CD with Radius 6.0 cm

1. How do you calculate the angular displacement of a CD with a radius of 6.0 cm?

To calculate the angular displacement, you will need to use the formula: θ = s/r, where θ is the angular displacement, s is the arc length, and r is the radius. In this case, s would be the length of the portion of the CD that has moved, and r is given as 6.0 cm.

2. What is the unit of measurement for angular displacement?

The unit of measurement for angular displacement is radians (rad) or degrees (°). Radians are the preferred unit for scientific calculations, while degrees are more commonly used in everyday situations.

3. Can the angular displacement be negative?

Yes, the angular displacement can be negative. This indicates that the object has rotated in the clockwise direction. A positive angular displacement indicates a counterclockwise rotation.

4. How is the angular displacement of a CD different from its linear displacement?

The angular displacement of a CD is a measure of the rotation of the CD around its center, while the linear displacement is a measure of the distance the CD has moved in a straight line. In other words, the angular displacement tells you how much the CD has turned, while the linear displacement tells you how far it has traveled.

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

Angular displacement and angular velocity are related by the formula: ω = Δθ/Δt, where ω is the angular velocity, Δθ is the change in angular displacement, and Δt is the change in time. In other words, angular velocity is the rate at which the angular displacement is changing over time.

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