# Rotational Kinematics of a disc

1. Nov 8, 2009

### mattmannmf

How far has the disk moved?

Disk has .34m radius with a mass of 7.4. The angular acceleration about the center of mass is 100.2 rad/s2.

So this is what i did:
ang. disp= .5(ang. accel)*t^2
(x=.5(a)t^2 =>pretty much)

I got my ang. disp to be 84.669 rad. Now i need to convert it to meters.
The circum. of the circle i got was 2.136 (2(pi)r= 2*3.1415*.34). so thats how far it goes in 1 revolution.

So i do 84.669rad* (1 rev/(2(pi) rad) * (2.136 m/ 1 rev)..... so (84.669*2.136)
/ (2(pi))

I got the answer to be 28.78 m...and when i checked it was wrong...no idea where i went wrong

Also the 2nd part of the question asks what is the translational speed of the disk... i have no idea what translational speed is or means. please help!!

2. Nov 8, 2009

### hage567

Were you given a value for time? Could you state the entire question as it was given to you?

3. Nov 8, 2009

### mattmannmf

A solid uniform disk of mass M = 7.4 kg and radius R = 34 cm rests with its flat surface on a frictionless table (i.e., the axis of the cylinder is perpendicular to the table.) The diagram shows a top view. A string is wrapped around the rim of the disk and a constant force of F = 126 N is applied to the string. The string does not slip on the rim.

a) What is the acceleration of the center of mass?
a = m/s2 *
17.03 OK

HELP: Draw a free-body diagram and apply Newton's Second Law.

b) What is the angular acceleration about the center of mass?
100.2 OK

HELP: Draw a free-body diagram, find the torque, and apply the rotational analog of Newton's 2nd Law.

The next 5 questions refer to a time 1.3 s after the force is first applied.
c) How far has the disk moved?
d = m
28.783 NO

HELP: This is a problem in one-dimensional kinematics.
HELP: We have a constant acceleration, so we can use our standard kinematics formulas to find out the distance traveled in a given time.

d) Through what angle has the disk turned?
84.669 OK

e) What is the translational speed of the disk?

4. Nov 8, 2009

### hage567

I think you are missing a factor of two somewhere.

Translation in this case just means as it moves across the table.

5. Nov 8, 2009

### mattmannmf

missing a factor of 2? i dont know... like the math seems right. Maybe i am off by a little bit due to rounding error?

6. Nov 8, 2009

### mattmannmf

yes..where I= .5*m*r^2