Questions regarding rotational motion

[dismalice]

Homework Statement

A computer disk is 8.0 cm in diameter. A reference dot on the edge of the disk is initially located at The disk accelerates steadily for 0.50 s, reaching 2000 rpm, then coasts at steady angular velocity for another 0.50 s.

I have found that a_t=17 m/s^2 @ .25s
a_c = 440 m/s^2 @ .25s
and v = 8.4 m/s @ 1s
I need to find the angular position of the reference dot @ t=1s

Homework Equations

Theta = Theta(not) + (Alpha T^2)/2
s=rTheta

The Attempt at a Solution

Alpha= dW/dT = 2000 (2pi/60) = 209.44 rad/s

Theta= 0+ ((alpha)t^2)/2) + (alpha*t^2) = 314.16 rad

 

[Delphi51]

I think you have to do it in two parts.
First the accelerated part, then the constant speed part.
No one formula applies to the whole motion.

 

[dismalice]

I think you have to do it in two parts.
First the accelerated part, then the constant speed part.
No one formula applies to the whole motion.

Could you please give me an example, I am not quite clear on what you are saying.

 

[Delphi51]

For the first .5 seconds, it is accelerated, so use your
Theta= 0+ ((alpha)t^2)/2) + (alpha*t^2)
Oops, I don't think that is quite right - better look it up.
I think the rotational formulas are analagous to the linear ones, so think
D = V1*t + ½ at²
and change the D to θ, the V1 to ω1, the a to alpha.

The formula for the second part will be analgous to d = vt.

 

[rwisz]

The angular position of the reference dot at t=1s would be 314.16 radians. This can be calculated using the formula Theta = Theta(not) + (Alpha T^2)/2, where Alpha is the angular acceleration and T is the time. In this case, the initial angular position (Theta(not)) is 0, and the time is 1 second. Therefore, the angular position at t=1s would be 314.16 radians. This makes sense because the disk is rotating at a constant angular velocity, so the angular position would increase linearly with time.