Object rolling down an incline

In summary, the problem involves a solid sphere of radius 20cm on an incline of 22 degrees with an initial vertical distance of 1.8m. The moment of inertia for the sphere is given as 2/3MR^2. The task is to calculate the speed of the sphere when it reaches the bottom of the incline, assuming it slips without rolling. The relevant equations are mgh = 1/2Iw^2 + 1/2mv^2 and v = \omega r, and the solution does not involve rotational kinetic energy.
  • #1
Momentum09
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Homework Statement



A solid sphere of radius 20cm is positioned at the top of an incline that makes 22 degrees angle with the horizontal. This initial position of the sphere is a vertical distance 1.8m above its position when at the bottom of the incline. Moment of inertia of a sphere with respect to an axis through its center is 2/3MR^2. Calculate the speed of the sphere when it reaches the bottom of the incline in the case where it slips frictionlessly without rolling.

Homework Equations



mgh = 1/2Iw^2 + 1/2mv^2

The Attempt at a Solution



I know how to calculate the speed when the object rolls down without slipping, but what do I do if it does? if there a formula? Thank you for your help!
 
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  • #2
If it slips without rolling then there is no rotational KE, just translational KE.

If it rolls without slipping then there is both rotational and translational KE. The are related by the condition for "rolling without slipping", which is: [itex]v = \omega r[/itex].
 
  • #3
Thank you so much!
 

1. What factors affect the speed of an object rolling down an incline?

The speed of an object rolling down an incline is affected by the angle of the incline, the mass of the object, and the force of gravity.

2. How does the angle of the incline affect the acceleration of an object rolling down?

The steeper the incline, the greater the acceleration of the object. This is because the force of gravity pulling the object down the incline is greater at steeper angles.

3. Does the shape of the object affect its rolling motion down an incline?

Yes, the shape of the object can affect its rolling motion down an incline. Objects with a rounder shape tend to roll more smoothly and have less friction, resulting in a faster speed.

4. What is the relationship between the mass of an object and its acceleration down an incline?

The mass of an object has an inverse relationship with its acceleration down an incline. This means that as the mass of the object increases, its acceleration decreases.

5. Can the rolling motion of an object down an incline be affected by external forces?

Yes, external forces such as air resistance or friction can affect the rolling motion of an object down an incline. These forces can slow down or speed up the object, depending on their direction and magnitude.

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