Hoop and disk rolling(help )

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In summary, the conversation discusses the problem of determining the speeds and ratio of accelerations of a uniform solid disk and hoop as they roll down an incline without slipping. Based on the equations and calculations provided, the ratio of their accelerations is 4/3.
  • #1
Mac13
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hoop and disk rolling(help please)

ok I've been looking at this forever and can't get it...dont know what to do..i would appreciate it if someone could help

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A uniform solid disk and a uniform hoop are
placed side by side at the top of an incline of
height h.
If they are released from rest and roll with-
out slipping, determine their speeds when
they reach the bottom. (here i found the speeds to be
velocity disk = sqrt(4/3hg)
velocity hoop = sqrt(hg)

now here is my problem

What is the ratio of their accelerations as they
roll down the incline, a_disk / a_hoop?

1. 4/3
2. 2
3. sqrt(3)
4. sqrt(3/2)
5. 1/2 xxxx
6. sqrt(4/3)
7. 1/3 xxxx
8. 3
9. 3/2
10. sqrt(2)

..ps - the ones i put an xxxx out the right on i figured couldn't be it since the velocity of the disk is greater the acceleration of the disk(top value) must be greater
 
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  • #2
Mac13 said:
If they are released from rest and roll with-
out slipping, determine their speeds when
they reach the bottom. (here i found the speeds to be
velocity disk = sqrt(4/3hg)
velocity hoop = sqrt(hg)

now here is my problem

What is the ratio of their accelerations as they
roll down the incline, a_disk / a_hoop?

1. 4/3
2. 2
3. sqrt(3)
4. sqrt(3/2)
5. 1/2 xxxx
6. sqrt(4/3)
7. 1/3 xxxx
8. 3
9. 3/2
10. sqrt(2)

Write the acceleration for each
disk: sqrt(4/3hg)/t
hoop: sqrt(hg)/t

Now divide them and see what you get.
disk/hoop = sqrt(4/3) which is answer 6

You remember how to divide radicals right?
 
Last edited:
  • #3
ShawnD's answer isn't quite correct. Because the two objects are rolling down with a different acceleration, there is a difference in time in order to get to the bottom. However, regardless, we do know the equation

[tex]v_f^2 = v_i^2 + 2ad[/tex]
In case LaTeX doesn't work, v_f^2 = v_i^2 + 2ad,

both initial velocities are zero, so we solve for a in terms of v_f and get

[tex]a = \frac{v_f^2}{2d}[/tex]
a = v_f^2/(2d)

Since d is the same for both, we can compare these two velocities, so our answer will come from

a1/a2 = (v_f1/v_f2)^2 = (Sqrt[4/3hg]/Sqrt[hg])^2 = Sqrt[4/3]^2 = 4/3

cookiemonster
 

1. What is the difference between hoop and disk rolling?

Hoop rolling is the motion of a circular object with a uniform mass distribution, while disk rolling is the motion of a solid object with a non-uniform mass distribution. This results in different rotational and translational velocities for each type of rolling.

2. How does the radius of the hoop or disk affect its rolling motion?

The radius of the hoop or disk affects its moment of inertia, which is a measure of the object's resistance to rotational motion. A larger radius results in a larger moment of inertia and therefore a slower rolling motion.

3. What is the role of friction in hoop and disk rolling?

Friction plays a crucial role in hoop and disk rolling as it provides the force necessary for the object to roll. Without friction, the object would simply slide without any rotational motion. The coefficient of friction between the object and the surface it is rolling on also affects its rolling motion.

4. How does the surface on which the hoop or disk is rolling affect its motion?

The surface on which the object is rolling can affect its motion in several ways. A rough surface will result in more friction and potentially slower rolling motion, while a smooth surface will result in less friction and potentially faster rolling motion. Additionally, the surface's incline or slope can also affect the object's velocity and acceleration.

5. Can the motion of a hoop or disk be predicted using equations?

Yes, the motion of a hoop or disk can be predicted using equations from rotational dynamics. These equations take into account factors such as the object's moment of inertia, angular velocity, and external forces, allowing for the prediction of its rolling motion. However, these equations may not always accurately predict the exact motion due to factors such as surface conditions and air resistance.

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