Rotational Kinematics of a disc

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Homework Help Overview

The discussion revolves around the rotational kinematics of a disk, specifically focusing on the distance traveled by the disk and its translational speed. The problem involves a disk with a specified radius and mass, subjected to angular acceleration.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts to calculate the distance moved by the disk using angular displacement and conversion to linear distance, but expresses confusion over the correctness of their result. They also seek clarification on the concept of translational speed.
  • Some participants question the need for a time value and request the full problem statement for clarity.
  • Another participant suggests that the original poster may be missing a factor of two in their calculations.
  • There is mention of using kinematics formulas for constant acceleration to find the distance traveled.

Discussion Status

The discussion is ongoing, with participants exploring various interpretations of the problem. Some guidance has been offered regarding the use of free-body diagrams and Newton's laws, but there is no explicit consensus on the calculations or the correct approach to the problem.

Contextual Notes

The problem includes a specific time frame of 1.3 seconds after a force is applied, and there are indications that assumptions about the setup may need to be revisited.

mattmannmf
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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 that's 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!
 
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Were you given a value for time? Could you state the entire question as it was given to you?
 
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?
a = rad/s2 *
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?
q = rad *
84.669 OK

e) What is the translational speed of the disk?
 
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
I think you are missing a factor of two somewhere.

e) What is the translational speed of the disk?
Translation in this case just means as it moves across the table.
 
missing a factor of 2? i don't know... like the math seems right. Maybe i am off by a little bit due to rounding error?
 
yes..where I= .5*m*r^2
 

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