Help with rotation/inertia problem

• dimitri24
In summary, Daniel is trying to figure out how to calculate the ball's velocity when it's on an incline, and how to account for friction.
dimitri24
lets say that:
a ball rolls on flat surface at a constant velocity towards an inclined plane

how would u answer the following, this is very confusing for me. i don't have the exact values =/

a)calculate KEtotal before it gets to the plane
b)calculate linear velocity when it makes it up to the top of the inclined plane
c)find out how far it falls after it leaves the inclined plane
d)and if the inclined plane were frictionless, would the ball's speed at the top of the incline be greater than, equal to, or less than the speed you already calculated

this is the best i can remember off the top of my head. any help is appreciated, thx

Okay.Rolling without slipping surely makes life easier,metaphorically speaking.

U have a rigid body which undergoes both rotation & translation movement.What's the total KE...?

Daniel.

P.S.The problem doesn't say it explicitely,but u know the initial velocity & and the mass & the radius of the ball.

(1/2)(Icm)(w^2) + (1/2)(M)(Vcm^2) ?

Perfect.For point b),u need to apply the total mechanical energy conservation law.

Daniel.

im not familiar with that, is it easy to explain? thanks

Well,in the absence of any external forces,the total energy of the system formed by Earth & sphere is conserved (a theorem following from Newton's axioms).

Assuming the Earth to have an $\infty$ mass,this law can be written for the sphere only.

Intially u have KE and 0 PE,atop the ramp u have $\neq 0$ KE & PE.U know that the sum of both is the same,both at the botton of the ramp & atop.

Daniel.

but how do u account friction into the equation when the ball is going up the incline. how would i attack part b?

Well,energy is conserved in part b).So solve part b) and then worry about the friction on the incline.

Daniel.

dimitri24 said:
but how do u account friction into the equation when the ball is going up the incline. how would i attack part b?
Since the ball is assumed to roll up the incline without slipping, no energy is wasted doing work against friction. (It's static friction.) So, as Daniel says, mechanical energy is conserved.

Hint: What's the relationship between $\omega$ and the translational speed v when the ball "rolls without slipping"?

1. What is rotational inertia and why is it important?

Rotational inertia, also known as moment of inertia, is a measure of an object's resistance to changes in its rotational motion. It is important because it determines how much torque is needed to change the object's angular velocity.

2. How is rotational inertia different from mass?

Mass is a measure of an object's resistance to changes in its linear motion, while rotational inertia is a measure of its resistance to changes in its rotational motion. They are not the same, but they are related through the object's shape and distribution of mass.

3. What factors affect rotational inertia?

The factors that affect rotational inertia include the mass of the object, the distance of the mass from the axis of rotation, and the shape of the object. Objects with more mass, mass further from the axis, and a larger radius of gyration will have a higher rotational inertia.

4. How can I calculate rotational inertia?

The formula for calculating rotational inertia depends on the shape of the object. For a point mass, it is simply the mass multiplied by the square of the distance from the axis of rotation. For more complex shapes, such as a solid cylinder or a hollow sphere, there are specific formulas that can be used.

5. How does rotational inertia affect rotational motion?

The higher the rotational inertia of an object, the more difficult it is to change its rotational motion. This means that objects with higher rotational inertia will require more torque to start rotating, and will also resist changes in their rotational speed. Rotational inertia also plays a role in the stability and balance of rotating objects.

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