Angular acceleration of a skater

The textbook gives a value of -17 rad/s2, while Bbrad sue calculated -18 rad/s2 using the formula \omega^2 \ = \ {\omega^2}_o \ + \ 2\alpha \ \Delta\theta. The angular equivalent of the formula v^2 \ = \ {v^2}_o \ + \ 2as is used to calculate the magnitude of the angular deceleration. The final answer of -17 rad/s2 is rounded.
  • #1
brad sue
281
0
Hi,
I need help with the following problem.

A skater does a pirouette at the rate of 2.0 rev / second and then stop within 3/4 rev. Assume that the angular decceleration is constant and calculate its magnitude.

I tried to compute it but I found -18 rad/s2.
BUt the textbook gives -17 rad/s2.
Please can someone help me with this problem?

Thank you
B
 
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  • #2
brad sue,
use
[tex]\omega^2 \ = \ {\omega^2}_o \ + \ 2\alpha \ \Delta\theta[/tex]
The rotational equivalent of
[tex]v^2 \ = \ {v^2}_o \ + \ 2as[/tex]
 
Last edited:
  • #3
What formula did you use to compute 18 rad/s2?

What is the angular analogy to v2 = vo2 + 2ax?

The 17 rad/s would be rounded.
 
  • #4
Astronuc said:
What formula did you use to compute 18 rad/s2?
What is the angular analogy to v2 = vo2 + 2ax?
The 17 rad/s would be rounded.

Yes the -17 has been rounded.
Thank you very much you all..

B
 

FAQ: Angular acceleration of a skater

What is angular acceleration?

Angular acceleration is the rate of change of angular velocity, which is the speed at which an object is rotating around a fixed axis.

How is angular acceleration different from linear acceleration?

Angular acceleration is specific to rotational motion and describes how an object's angular velocity changes over time. On the other hand, linear acceleration refers to the change in an object's linear velocity, or speed and direction of motion, over time.

How is angular acceleration calculated?

Angular acceleration is calculated by dividing the change in angular velocity by the change in time. It is represented by the symbol alpha (α) and has units of radians per second squared (rad/s²).

What factors affect the angular acceleration of a skater?

The angular acceleration of a skater can be affected by several factors, including the torque applied by the skater's muscles, the skater's moment of inertia (how mass is distributed around their body), and any external forces acting on the skater (such as friction or air resistance).

How does angular acceleration impact a skater's performance?

Angular acceleration plays a crucial role in a skater's performance as it determines how quickly they can change the direction of their rotation, leading to more complex and impressive maneuvers. A higher angular acceleration also allows skaters to spin faster and more smoothly.

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