Angular Frequency of Uniform Disk | Calculation & Solution

In summary, The problem involves a uniform disk suspended from a pivot. The equation w = sqrt (k/m) can be used to find the angular frequency for small oscillations, but the moment of inertia needs to be considered for this physical pendulum. The parallel axis theorem can be used to find the moment of inertia of the disk about the pivot point.
  • #1
Momentum09
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Homework Statement



A uniform disk of radius 1.4m and mass 2.6kg is suspended from a pivot 0.35m above its center of mass. Find the angular frequency w for small oscillations.

Homework Equations



w = 2 x pi x f = sqrt (k/m)

The Attempt at a Solution



Is this the equation I would use to solve this problem? Or does moment of inertia have to be considered also?
 
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  • #2
This is a physical pendulum. (Look it up!) You'll need to compute the rotational inertia about the pivot point.
 
  • #3
Use the parallel axis theorem to find the moment of inertia of the disk about the pivot point.
 

FAQ: Angular Frequency of Uniform Disk | Calculation & Solution

What is the formula for calculating the angular frequency of a uniform disk?

The formula for calculating the angular frequency (ω) of a uniform disk is ω = √(g/R), where g is the acceleration due to gravity and R is the radius of the disk.

How do you find the angular frequency of a disk with a given mass and radius?

To find the angular frequency of a disk with a given mass and radius, you can use the formula ω = √(g/R), where g is the acceleration due to gravity and R is the radius of the disk. Make sure to use consistent units for mass and radius (e.g. kilograms and meters).

What is the unit of measurement for angular frequency?

The unit of measurement for angular frequency is radians per second (rad/s).

How does the angular frequency of a uniform disk affect its rotational motion?

The angular frequency of a uniform disk determines how fast the disk rotates. A higher angular frequency means the disk will rotate faster, and a lower angular frequency means the disk will rotate slower.

Can the angular frequency of a uniform disk change over time?

Yes, the angular frequency of a uniform disk can change over time if external forces are applied to the disk, such as a torque. However, in the absence of external forces, the angular frequency will remain constant due to the conservation of angular momentum.

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