Solve Rotation Questions: 2.53 Revs in 6.28 & 19.3 Secs

[shell4987]

Homework Statement

A merry-go-round rotates from rest with an angular acceleration of 1.65 rad/s2. How long does it take to rotate through (a) the first 2.53 rev and (b) the next 2.53 rev?

Homework Equations

The Attempt at a Solution

I tried to do this and I converted the rev to radians by multiplying the revolutions by 2pi and then for (a) I divided 15.896/1.65 and got 6.28 seconds (15.896 is 2.53(2pi))and for (b) I divided 31.79/1.65 to get 19.3 seconds. What am I doing wrong here?

 

[hage567]

I divided 15.896/1.65 and got 6.28 seconds

Check your units, this doesn't work out to seconds.

What equation relates time, angular displacement, and angular acceleration?

 

[shell4987]

Check your units, this doesn't work out to seconds.

What equation relates time, angular displacement, and angular acceleration?

theta-theta initial= w initial(t) + (1/2)at^2?

 

[hage567]

What do you get for the time with that equation?

 

[shell4987]

What do you get for the time with that equation?

For (a) I got 1.75seconds and for (b) I got 2.48 seconds. I used 2.53 as the first displacement and for w I put in 0 and for acceleration I put 1.65 and then solved for t and that's what I got, and for the second part I put in 5.06 for the displacement. What am I doing wrong?

 

[hage567]

I used 2.53 as the first displacement

You need to change this into radians before using it in your calculations. Your units are not consistent otherwise. Try part (a) again with that change.