Speed of Point on Rim of 50.0 g Disk with 8.00 cm Diameter

In summary, the problem involves a thin disk with a mass of 50.0 g and a diameter of 8.00 cm rotating about its center with 0.190 J of kinetic energy. To find the speed of a point on the rim, the formula v=r\omega is used, with r being the radius of the disk and \omega being the angular speed. By substituting the given values into the formula, the correct answer of 3.9 m/s is obtained.
  • #1
tangibleLime
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0

Homework Statement


A thin, 50.0 g disk with a diameter of 8.00 cm rotates about an axis through its center with 0.190 J of kinetic energy. What is the speed of a point on the rim?

Homework Equations


[tex]C = \frac{1}{2}MR^2[/tex]
[tex]K_{rot}=\frac{1}{2}I\omega^2[/tex]

The Attempt at a Solution


Since the formula for kinetic rotational energy is [tex]K_{rot}=\frac{1}{2}I\omega^2[/tex], and the constant for the moment of inertia for a solid disk with the axis of rotation about it's diameter is [tex]C = \frac{1}{2}MR^2[/tex], I substituted the I in the second equation with the first equation, resulting in the following:

[tex]K_{rot}=\frac{1}{2}(\frac{1}{2}MR^2)\omega^2[/tex]

Substituting the values that I was supplied with in the problem statement, I came up with this equation:

[tex]0.190=\frac{1}{2}(\frac{1}{2}(0.05)(0.04)^2)\omega^2[/tex]

Solving for [tex]\omega[/tex], I ended up with [tex]\omega \approx \pm 97.5[/tex], which was determined to be incorrect.

Any help would be extremely appreciated.
 
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  • #2
It asks for the SPEED of a point on the rim. It does not ask for the angular speed.
 
  • #3
I figured it was something like that, so shortly after posting the initial topic, I tried [tex]v=r\omega[/tex] as [tex]v=(0.04)(97.5)[/tex] which results in the correct answer of 3.9. Originally I received an answer that was something like 360 (I must have entered a wrong number or something into the calculator) so I ignored it. Then after you posted and backed up my thoughts, I tried again and got the correct answer. Thanks!
 

1. What is the equation for calculating the speed of a point on the rim of a 50.0 g disk with 8.00 cm diameter?

The equation for calculating the speed of a point on the rim of a disk is v = ωr, where v is the linear speed, ω is the angular velocity, and r is the radius of the disk.

2. How do you determine the angular velocity of a rotating disk?

The angular velocity of a rotating disk can be determined by dividing the number of revolutions (or rotations) per unit of time. It is typically measured in radians per second.

3. What is the relationship between linear speed and angular velocity in a rotating disk?

The linear speed of a point on the rim of a rotating disk is directly proportional to the angular velocity of the disk. As the angular velocity increases, the linear speed of the point on the rim also increases.

4. What factors can affect the speed of a point on the rim of a rotating disk?

The speed of a point on the rim of a rotating disk can be affected by the angular velocity of the disk, the radius of the disk, and any external forces acting on the disk (such as friction or air resistance).

5. How does the speed of a point on the rim of a rotating disk change if the disk's diameter is increased?

If the diameter of a rotating disk is increased, the speed of a point on the rim will also increase. This is because the linear speed is directly proportional to the radius of the disk, so a larger radius will result in a higher speed.

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