(Rotational Motion) Calculating maximum velocity.

In summary, the problem is to find the maximum velocity at which a spinning disk with an object of mass M placed at radius R and a coefficient of friction of μ will not slip. Two equations, V=sqrt(μ*r*g) and V=sqrt((μ*g)/R), have been found online but it is unclear which one is correct. It is suggested to derive a new equation by drawing a free body diagram of the object and making an attempt at the solution. The equations found online may not be appropriate for this specific scenario and need more context and definitions of variables.
  • #1
KANY3EUWEST
1
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Homework Statement


If I have an object with mass M. Place it on a spinning disk at radius R and the coefficient of friction is μ what is the maximum velocity I can spin the disk without the object slipping? I have the actual values for the problem, but I'm much more interested in how to get there.

Homework Equations


I've found two equations online that pertain to this scenario, but they're completely different. V=sqrt(μ*r*g) and V=sqrt((μ*g)/R)

The Attempt at a Solution


I haven't made an attempt as I'm not exactly sure which equation to use, or if either are correct.
 
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  • #2
Where did you find these equations? Under what conditions were they derived?
I suggest that you derive your own equation. Start by drawing a free body diagram of the object at the moment when it is just about ready to slip. So make an attempt and post it.

On edit: One of the two equations you posted is not even appropriate to be a velocity. Which one is it?
 
  • #3
KANY3EUWEST said:
V=sqrt(μ*r*g) and V=sqrt((μ*g)/R)
Equations are meaningless out of context. They need to be accompanied by definitions of the variables and a description of the circumstances in which they are valid.
Are such provided at those links? Do they match the circumstance you have?
As kuruman points out, if in those equations the variables stand for what one would guess, one of them is dimensionally wrong. Which one?
 

1. What is rotational motion and how is it different from linear motion?

Rotational motion refers to the movement of an object around an axis or center point. It is characterized by circular or curved paths. In contrast, linear motion involves movement in a straight line.

2. How is maximum velocity calculated in rotational motion?

The maximum velocity in rotational motion can be calculated using the equation v = ωr, where v is the linear velocity, ω is the angular velocity, and r is the distance from the axis of rotation. This equation relates the rotational and linear velocities of an object.

3. What factors affect the maximum velocity in rotational motion?

The maximum velocity in rotational motion is affected by the angular velocity, the distance from the axis of rotation, and the mass of the object. The angular velocity and distance have a direct relationship with maximum velocity, while the mass has an inverse relationship.

4. Can the maximum velocity in rotational motion be greater than the linear velocity?

Yes, the maximum velocity in rotational motion can be greater than the linear velocity. This is because the linear velocity only measures the speed of an object in a straight line, while the maximum velocity in rotational motion takes into account the distance from the axis of rotation, which can be much greater.

5. How is the concept of torque related to calculating maximum velocity in rotational motion?

Torque is the measure of the force that causes an object to rotate around an axis. The greater the torque, the faster an object will rotate, resulting in a higher maximum velocity. Therefore, torque is an important factor to consider when calculating the maximum velocity in rotational motion.

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