Rotational Kinematics Problem - find the angular displacement

[grandprix]

Homework Statement

The drive propeller of a ship starts from rest and accelerates at 2.90e-3 rad/s^2 for 2.1e3 seconds. For the nest 1.4e3 seconds, the propeller rotates at a constant angular speed. Then it decelerates at 2.3e-3 rad/s^2 until it slow (without reversing direction) to an angular speed of 4.0 rad/s. Find the total angular displacement of the propeller.

Homework Equations

a) w(t) = w0 + (alpha*time)

The Attempt at a Solution

Basically i used equation a) to solve for displacement for the first 2100 seconds, then for the next 1400 seconds I used equation a) and first found w0, and then plugged that value into theta= theta0+ w0*t +(1/2 alpha*time)

I took both these values and added them together.

 

[tiny-tim]

Welcome to PF!

Hi grandprix! Welcome to PF!

(have an omega: ω and a theta: θ and an alpha: α and try using the X² tag just above the Reply box )

The drive propeller of a ship starts from rest and accelerates at 2.90e-3 rad/s^2 for 2.1e3 seconds. For the nest 1.4e3 seconds, the propeller rotates at a constant angular speed. Then it decelerates at 2.3e-3 rad/s^2 until it slow (without reversing direction) to an angular speed of 4.0 rad/s. Find the total angular displacement of the propeller.
…
a) w(t) = w0 + (alpha*time)
…
Basically i used equation a) to solve for displacement for the first 2100 seconds, then for the next 1400 seconds I used equation a) and first found w0, and then plugged that value into theta= theta0+ w0*t +(1/2 alpha*time)

I took both these values and added them together.

You seem to have the equations the wrong way round …

(and anyway it should be theta= theta0+ w0*t +(1/2 alpha*time-squared) )

just use the standard constant acceleration equations in the usual way, but with θ ω and α instead of s v and a

 

[grandprix]

oh thank you so much! I tried to make the solution a lot more complicated than it is i guess.. and thank you for letting me know about where to find all the proper notations!