- #1
BrianSauce
- 17
- 1
This is the second part of a 2 part problem. The first part is:
A solid disc is rolling down a 30 degree incline from rest.
a. draw the force diagram for the disk.
b. write the equations for both translation and rotational motion
c. Find the linear acceleration of the center of mass.
d. If the radius of the disk is r, find the angular acceleration of the disk.
e. If the mass of the disc is m, what is the expression for the friction force?
I solved b. as: Translation {mgsin[itex]\varphi[/itex]-fs = ma , N=mgcos[itex]\varphi[/itex]} Rotation: fr=I[itex]\alpha[/itex]
For c my answer was a=g/3
For d I got [itex]\alpha[/itex]=2f/mr
And for e I got f= mg/6
Now part 2 says, "In the previous problem the disk started to roll from a height of h=2m with no initial velocity. Use the answers from part 1 to find:
a. The time to reach the bottom of the incline.
b. The velocity of its c.m. at the bottom of the incline.
c. The angular speed of the disk at the bottom of the incline if the radius of the disc is 25cm.
This is where I am stumped. I tried solving for the velocity by using Kinetic Energy, mgh = 1/2 I[itex]\omega[/itex]^2 + 1/2mv^2
But I didn't get the correct answer. So I'm really lost, I tried Kinematic but just got lost not sure which equations to use.
A solid disc is rolling down a 30 degree incline from rest.
a. draw the force diagram for the disk.
b. write the equations for both translation and rotational motion
c. Find the linear acceleration of the center of mass.
d. If the radius of the disk is r, find the angular acceleration of the disk.
e. If the mass of the disc is m, what is the expression for the friction force?
I solved b. as: Translation {mgsin[itex]\varphi[/itex]-fs = ma , N=mgcos[itex]\varphi[/itex]} Rotation: fr=I[itex]\alpha[/itex]
For c my answer was a=g/3
For d I got [itex]\alpha[/itex]=2f/mr
And for e I got f= mg/6
Now part 2 says, "In the previous problem the disk started to roll from a height of h=2m with no initial velocity. Use the answers from part 1 to find:
a. The time to reach the bottom of the incline.
b. The velocity of its c.m. at the bottom of the incline.
c. The angular speed of the disk at the bottom of the incline if the radius of the disc is 25cm.
This is where I am stumped. I tried solving for the velocity by using Kinetic Energy, mgh = 1/2 I[itex]\omega[/itex]^2 + 1/2mv^2
But I didn't get the correct answer. So I'm really lost, I tried Kinematic but just got lost not sure which equations to use.