Maximum angular velocity of disc skidding across surface

In summary, the problem involves finding the maximum angular velocity attained by a saucer with a coefficient of kinetic friction of 0.42, gravity of 10.6 m/s, and a disk mass of 1.75x10^9. The skid marks on the surface, which were 1280m long, were caused by uneven friction that resulted in slow rotation around the saucer's principal axis. Using the approximation of the saucer as a solid disk, the maximum angular velocity can be found using the equation Sqrt [(4/r^2)* (.42*10.6*1280 - (1/2)Vi^2) ] = w. The listed answer is 0.23, but the
  • #1
rickyjoepr
6
1

Homework Statement


coefficient of kinetic friction between the disk and the surface is 0.42

gravity = 10.6 m/s
disk mass = 1.75x10^9

the skid marks are 1280m long, This is due to the fact that uneven friction had set the saucer in very slow rotation around its principal axis. By approximating the saucer by a solid disk, what is the maximum angular velocity attained during the skid?

Homework Equations



Ke = (.5)(I*w^2)

The Attempt at a Solution



fk*d = Ke

(.42)(1.75x10^9)(10.6)(1280) = (1/4)(mr^2)*w^2)

masses will cancel

Sqrt[(4)(.42)(10.6)(1280)(1/r^2)] = w

i get .926

but the listed answer is .23

Not sure If I am approaching this correctly
 
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  • #2
got it

Fk*d = ((.5)mVi^2) + (.5)((Iw^2)

eventually simplified to

Sqrt [ (4/r^2)* (.42*10.6*1280 - (1/2)Vi^2) ] = w
 

1. What is the maximum angular velocity of a disc skidding across a surface?

The maximum angular velocity of a disc skidding across a surface is dependent on several factors such as the coefficient of friction between the disc and the surface, the mass and radius of the disc, and the applied force. It can be calculated using the formula v = Ωr, where v is the linear velocity, Ω is the angular velocity, and r is the radius of the disc.

2. How does the coefficient of friction affect the maximum angular velocity of a disc skidding?

The coefficient of friction is a measure of the resistance between two surfaces in contact. A higher coefficient of friction means that there is more resistance, and therefore, a lower maximum angular velocity. This is because the force required to overcome the friction increases as the angular velocity increases.

3. Can the maximum angular velocity of a disc skidding be exceeded?

Technically, yes, the maximum angular velocity can be exceeded. However, this can lead to the disc slipping or sliding instead of skidding, which can be dangerous and cause loss of control. It is important to stay within the calculated maximum angular velocity to ensure safe and controlled movement of the disc.

4. How does the mass and radius of the disc affect the maximum angular velocity?

The mass and radius of the disc have a direct impact on the maximum angular velocity. A larger and heavier disc will require more force to overcome the friction and reach a certain angular velocity. Therefore, a disc with a larger mass and radius will have a lower maximum angular velocity compared to a lighter and smaller disc.

5. What is the relationship between linear velocity and angular velocity in a disc skidding?

In a disc skidding, the relationship between linear velocity and angular velocity is linear. This means that as the angular velocity increases, the linear velocity also increases proportionally. This relationship is described by the formula v = Ωr, where v is the linear velocity, Ω is the angular velocity, and r is the radius of the disc.

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