- #1
dzogi
- 11
- 0
1. First Problem
A disc with mass of 50kg and radius of 20cm is rotating with a frequency of 480rpm, and after 50 seconds, as a result of the force of friction, it stops. What's the moment (momentum of force, torque) if during the rotation the disc made 200 rotations?
[tex]M=I\epsilon[/tex]
[tex]R=0,2m; m=50kg; f=480min^{-1}=8Hz; t=50s; N=200;[/tex]
[tex]w_0=\frac{2\pi}{1/8}=16\pi rad/s[/tex]
[tex]w = 0rad/s[/tex]
[tex]\epsilon=\frac{w-w_o}{t}=\frac{-16\pi}{50}rad/s[/tex]
[tex]I=0.5mR^2=1[/tex]
[tex]M=I\epsilon=-1.21924Nm[/tex]
Is this correct? I can't see where to number of total rotations (angular distance) fits in, or maybe it's a distractor?
2. Second problem
А rope is wrapped around a horizontal cylinder with [tex]M=17kg; R=0,1m[/tex]. A bob with [tex]m=5kg[/tex] is attached at the end of the rope, at height of [tex]h=4m[/tex] above ground. The momentum of inertia of the cylinder is calculated with [tex]I=\frac{MR^2}{2}[/tex].
a) what's the speed of the bob when it hits ground?
b) calculate the total energy of the system.
I've solved b) pretty easily,
[tex]E=mgh=192,2J[/tex] which conforms to the solution in the book (so, the potential energy of the cylinder is ignored).
I've tried solving a) this way
[tex]mgh=\frac{mv^2}{2}+\frac{I\omega^2}{2}[/tex]
If the liner velocity of the cylinder is equal to the speed of the bob at any given time, then we can substitute [tex]\omega=\frac{v}{R}[/tex]
[tex]\vdots[/tex]
Is this approach correct? I don't get the same solution with the one given in the book.
Homework Statement
A disc with mass of 50kg and radius of 20cm is rotating with a frequency of 480rpm, and after 50 seconds, as a result of the force of friction, it stops. What's the moment (momentum of force, torque) if during the rotation the disc made 200 rotations?
Homework Equations
[tex]M=I\epsilon[/tex]
The Attempt at a Solution
[tex]R=0,2m; m=50kg; f=480min^{-1}=8Hz; t=50s; N=200;[/tex]
[tex]w_0=\frac{2\pi}{1/8}=16\pi rad/s[/tex]
[tex]w = 0rad/s[/tex]
[tex]\epsilon=\frac{w-w_o}{t}=\frac{-16\pi}{50}rad/s[/tex]
[tex]I=0.5mR^2=1[/tex]
[tex]M=I\epsilon=-1.21924Nm[/tex]
Is this correct? I can't see where to number of total rotations (angular distance) fits in, or maybe it's a distractor?
2. Second problem
Homework Statement
А rope is wrapped around a horizontal cylinder with [tex]M=17kg; R=0,1m[/tex]. A bob with [tex]m=5kg[/tex] is attached at the end of the rope, at height of [tex]h=4m[/tex] above ground. The momentum of inertia of the cylinder is calculated with [tex]I=\frac{MR^2}{2}[/tex].
a) what's the speed of the bob when it hits ground?
b) calculate the total energy of the system.
Homework Equations
The Attempt at a Solution
I've solved b) pretty easily,
[tex]E=mgh=192,2J[/tex] which conforms to the solution in the book (so, the potential energy of the cylinder is ignored).
I've tried solving a) this way
[tex]mgh=\frac{mv^2}{2}+\frac{I\omega^2}{2}[/tex]
If the liner velocity of the cylinder is equal to the speed of the bob at any given time, then we can substitute [tex]\omega=\frac{v}{R}[/tex]
[tex]\vdots[/tex]
Is this approach correct? I don't get the same solution with the one given in the book.
Last edited: