How Do You Calculate the Angular Velocity of a Disk?

In summary, the conversation discussed the problem of finding the angular velocity of a disk with a radius of 2.40 cm and mass of 1 kg, after being turned through 0.85 of a revolution and pulled by a string with a constant force of 0.36 Newtons. The solution involved converting the revolutions to degrees and then using the equations S=rθ, ∆x=R∆θ, W=F∆x, and conservation of work (W=∆K) to calculate the angular velocity. The individual seeking help was advised to check if they had converted the radius from centimeters to meters correctly.
  • #1
dalitwil
23
0
I already posted this somewhere, but silly me, i can't find it.

Q: A disk of radius 2.40 cm and mass 1 kg is pulled by a string wrapped around its circumference with a constant force of 0.36 Newtons. What is the angular velocity of the disk to three decimal places after it has been turned through 0.85 of a revolution?

So I started by obtaining my degrees from the 0.85 revolutions (S=rθ). This equals 2.225 degrees.

Next I used ∆x=R∆θ
(2.40)*(2.225)
=5.340 radians

W=F∆x
(0.36)*(5.340)
=1.9224

Using conservation of work (W=∆K):
K=.5Iω^2 (where I of a disk=.5MR^2)

W=1.9924=.5(.5*1*2.4^2)ω^2
ω=1.15542

WRONG. I can't figure out where I am going wrong, please help!
 
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  • #2
click your name in a thread like this, click view public profile, find all threads started by yourself. Find the thread
 
  • #3
Did you convert your 2.4 cm to meters?
 

FAQ: How Do You Calculate the Angular Velocity of a Disk?

What is angular velocity and why is it important in calculating disk rotation?

Angular velocity is a measure of how fast an object is rotating around a fixed axis. It is important in calculating disk rotation because it helps us understand the rate of change of the disk's orientation and allows us to determine its position at any given time.

How do you calculate angular velocity of a disk?

Angular velocity can be calculated by dividing the change in angle (in radians) by the change in time. The formula for angular velocity is ω = Δθ/Δt, where ω represents angular velocity, Δθ represents the change in angle, and Δt represents the change in time.

What units are used to measure angular velocity?

Angular velocity is typically measured in radians per second (rad/s) or degrees per second (°/s). However, it can also be measured in revolutions per minute (rpm) or revolutions per second (rps).

How does the radius of the disk affect its angular velocity?

The radius of the disk does not directly affect its angular velocity. However, it does affect the linear speed of a point on the disk's edge. The larger the radius, the greater the linear speed at that point, but the angular velocity remains the same.

Is there a difference between angular velocity and rotational speed?

Yes, there is a difference between angular velocity and rotational speed. Angular velocity is a vector quantity that describes the rate of change of the angular position of an object, while rotational speed is a scalar quantity that only describes how fast an object is rotating without specifying its direction.

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