What Is the Linear Speed of a Disk on an Inclined Plane?

  • Thread starter Jbreezy
  • Start date
  • Tags
    Energy
In summary, a solid disk of mass 2.5 kg and radius 11.0cm is released from rest on an incline plane with a height of 1.25 m and an angle of 25 degrees. Using the equation mgh = 1/2 mv^2 + 1/2Iw^2, the linear speed of the disk at the bottom of the incline can be calculated. After simplifying and substituting w = v/r, the equation becomes Sqrt(4/3gh) = v. Plugging in the given numbers, the linear speed is calculated to be 4.04 m/s. Different approaches may be used to solve the problem, but the important factor is knowing which
  • #1
Jbreezy
582
0

Homework Statement



A solid disk of mass 2.5 kg with a radius of 11.0cm is released from rest on an incline plane. If the plane is 1.25 m high and the angle is 25 degrees what will be the linear speed of the disk at the bottom of the incline?
Idisk = 1/2 mr^2 and Ihoop = mr^2

Homework Equations



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



The Attempt at a Solution


I = 1/2mr^2
mgh = 1/2 mv^2 + 1/2(1/2mr^2)w^2

mass cancles
gh = 1/2 v^2 + 1/4r^2w^2

substitute w = v/r

gh = 1/2 v^2 + 1/4r^2(v^2/r^2)

The radius will cancel you combine the velocity fraction get to v and you end up with something of the form

Sqrt(4/3gh) = v
Plug in the numbers and you get 4.04 m/s

Is this right? Please help me double check. I felt there was a lot of information that did not get used but that doesn't mean it is not correct.
Thanks,
j
 
Physics news on Phys.org
  • #2
Looks good to me.
 
  • #3
OK, well the more eyes the better. Thanks dude. It is just I feel he gave information to throw me off or something. I don't know.
 
  • #4
Jbreezy said:
It is just I feel he gave information to throw me off or something. I don't know.
Part of knowing how to solve a problem is knowing what's important and what's not.

And there are several ways to solve for the speed. What you did, solving it symbolically and only plugging numbers in at the last step, is the smart way. Someone else might have plugged numbers in at every step. The "unused" data would have been used by such a person.
 
  • #5
Yeah, It is right.
 
  • #6
Hi I have another one posted with torque and hanging a sign if someone oone could double check me it would be great. thanks for the help.
 

FAQ: What Is the Linear Speed of a Disk on an Inclined Plane?

What is rotational inertia?

Rotational inertia, also known as moment of inertia, is a measure of an object's resistance to changes in its rotational motion. It depends on the mass of the object and the distribution of that mass around its axis of rotation.

How is rotational inertia different from linear inertia?

Rotational inertia specifically refers to an object's resistance to changes in its rotational motion, while linear inertia refers to an object's resistance to changes in its linear motion. Rotational inertia depends on the object's shape and mass distribution, while linear inertia depends on the object's mass and velocity.

What is the relationship between rotational inertia and energy?

Rotational inertia and energy are related through the concept of angular momentum. As an object's rotational inertia increases, its angular momentum also increases, which means that more energy is required to change its rotational motion. Similarly, as an object's rotational speed increases, its kinetic energy also increases.

How does rotational inertia affect a spinning object?

Rotational inertia affects a spinning object by determining how much torque is needed to change its rotational motion. An object with a higher rotational inertia will require more torque to change its rotation, while an object with a lower rotational inertia will require less torque.

How is rotational inertia calculated?

Rotational inertia can be calculated using the formula I = mr^2, where I is the rotational inertia, m is the mass of the object, and r is the distance from the axis of rotation to the mass. This formula assumes that the object is a point mass, but for more complex objects, the moment of inertia can be calculated using integrals.

Back
Top