What Is the Correct Translational Velocity of a Disk Rolling Down an Incline?

In summary, to find the translational velocity of a disk released from rest on an incline, you can use the equation Kf + Uf = Ki + Ui, where Kf is the final kinetic energy, Uf is the final potential energy, Ki is the initial kinetic energy, and Ui is the initial potential energy. Substitute the given values of M, g, h, and R to solve for v. Using the moment of inertia of a disk, I=1/2MR^2, and the relationship between angular and linear velocity, ω=v/R, you can find the final kinetic energy in terms of M and v. This yields a final velocity of 17.1 m/s.
  • #1
alexito01
5
0

Homework Statement


A disk is released from rest from the top of an incline. The bottom of the incline is a vertical distance h=15m below the top. The wheel rolls without slipping. The moment of inertia of the disk is given by I=1/2MR2. What is the translational velocity of the disk at the bottom of the incline? (use g=9.8m/s2)


Homework Equations


PE= mgy and KE= 1/2mv^2 and ω=v/r


The Attempt at a Solution


I ended up with 17.1 m/s but it keeps telling me its wrong
 
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  • #2
Are you using rotational kinetic energy anywhere in your calculations? Notice that you were given the moment of inertia of a disk.
 
  • #3
Ki = 0
Kf = translation kinetic energy + rotational kinetic energy = 1/2 Mv^2 + 1/2 I w^2
In the above, substitute I = 1/2 MR^2 and w = v/R to find Kf in terms of M and v.

Ui = Mgy
Uf = 0
Kf + Uf = Ki + Ui
Substitute values and solve for v.
 

FAQ: What Is the Correct Translational Velocity of a Disk Rolling Down an Incline?

What is translational velocity?

Translational velocity refers to the rate at which an object's position changes over time, in a straight line.

How is translational velocity calculated?

Translational velocity is calculated by dividing the change in an object's position by the change in time.

What is the difference between translational velocity and speed?

The main difference between translational velocity and speed is that velocity takes into account the direction of the object's movement, while speed does not. Velocity is a vector quantity, while speed is a scalar quantity.

Why is translational velocity important in physics?

Translational velocity is important in physics because it is a fundamental property of motion and is used to describe the movement of objects in space. It is also a key factor in determining an object's kinetic energy and momentum.

How is translational velocity used in real-life applications?

Translational velocity is used in various real-life applications, such as designing and navigating spacecraft, calculating the speed and direction of projectiles, and analyzing the movement of vehicles and athletes in sports. It is also used in transportation systems to optimize travel time and fuel efficiency.

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