Disk and Block

1. Nov 30, 2004

Naeem

A uniform disk of mass Mdisk = 4.4 kg and radius R = 0.28 m has a small block of mass mblock = 2.4 kg on its rim. It rotates about an axis a distance d = 0.18 m from its center intersecting the disk along the radius on which the block is situated.

--------------------------------------------------------------------------------
a) What is the moment of inertia of the block about the rotation axis?
Iblock = kg*m2
2*0.18*0.18 NO

HELP: Remember: the block is on the rim of the disk.
HELP: The block is considered a point-mass.

--------------------------------------------------------------------------------
b) What is the moment of inertia of the disk about the rotation axis?
Idisk = kg*m2 *
4.4*0.28^2/2+4.4*0.18^2 OK

--------------------------------------------------------------------------------
c) When the system is rotating about the axis with an angular velocity of 5 rad/s, what is its energy?
KErot = J
(2.4*0.18^2+4.4*0.28^2/2+4.4*0.18^2)*5.0^2/2 NO

--------------------------------------------------------------------------------
d) If while the system is rotating with angular velocity 5 rad/s it has an angular acceleration of 8.4 rad/s2, what is the magnitude of the acceleration of the block?
|ablock| = m/s2
((5^2*0.18)^2+(8.4*0.18)^2)^(1/2) NO

2. Nov 30, 2004

arildno

a)
i) What is the mass of the block?
ii) What is the distance of the block to the rotation axis?
c)"(2.4*0.18^2+4.4*0.28^2/2+4.4*0.18^2)*5.0^2/2 NO"
Use the correct answer to aii)!

3. Nov 30, 2004

Naeem

OK, for a, here is what I did:
I = MR square
so,

I = Mblock * distance square
= 2.4 * 0.18 * 0.18 , but still the answer is wrong!!!!!

4. Nov 30, 2004

arildno

But the distance from the BLOCK to the rotation axis is 0.28-0.18=0.10

5. Nov 30, 2004

Naeem

OK, got that one can u help on c & d. Some inital guidance.

6. Nov 30, 2004

arildno

For c), you've used the wrong distance for the block.
On d) you should use:
$$||a||=\sqrt{r^{2}(\dot{\omega})^{2}+(r\omega^{2})^{2}}$$
where $$\omega$$ is the angulur velocity, $$\dot{\omega}$$ the angular acceleration, and r the radius to the rotation axis.

Note that this is just the formula you've been using but with the wrong radius value..

Last edited: Nov 30, 2004
7. Nov 30, 2004

Naeem

I got part d, need help with part c , then is the correct distance 0.10 m, if so,
is this correct:

2.4*0.10^2+4.4*0.28^2/2+4.4*0.10^2)*5.0^2/2

8. Nov 30, 2004

arildno

"2.4*0.10^2+4.4*0.28^2/2+4.4*0.10^2)*5.0^2/2"

"4.4*0.10^2"
Why did you change this value??
It should be, as it was initially 4.4*0.18^2

9. Nov 30, 2004

Naeem

The correct should be as follows: (2.4*0.10^2+4.4*0.28^2/2+4.4*0.18^2)*5.0^2/2

I got , this and all, thank you.!