What is the angular velocity at t = 2.4 sec based on given graph?

[SalsaOnMyTaco]

Homework Statement

The graph shows the angular velocity of a rotating wheel as a function of time.
https://online-s.physics.uiuc.edu/cgi/courses/shell/common/showme.pl?cc/DuPage/Phys1201/summer/homework/Ch-10-Rotation/ang_vel_graph/omega_vs_t-2.jpg

What is the angular displacement of the wheel at t = 2.4 sec?

Homework Equations

ωf=ωi+αt

θ=θ₀+ωit+1/2αt²

The Attempt at a Solution

I first try to find the acceleration it takes from initial angular velocity to move to t=2.4s
-6=-9+a(2.4)=1.25
α=1.25

so assuming θ₀=0

θ=-9(2.4)+1/2(1.25)(2.4)²
θ=-18?

 

[SalsaOnMyTaco]

any ideas? i also tried W=θ/t

 

[SalsaOnMyTaco]

what about bxh/2= 2.4*-6/2=-7.2 since the θ is the area is between above the line and the horitzonal x

 

[Chestermiller]

Homework Statement

The graph shows the angular velocity of a rotating wheel as a function of time.
https://online-s.physics.uiuc.edu/cgi/courses/shell/common/showme.pl?cc/DuPage/Phys1201/summer/homework/Ch-10-Rotation/ang_vel_graph/omega_vs_t-2.jpg

What is the angular displacement of the wheel at t = 2.4 sec?

Homework Equations

ωf=ωi+αt

θ=θ₀+ωit+1/2αt²

The Attempt at a Solution

I first try to find the acceleration it takes from initial angular velocity to move to t=2.4s
-6=-9+a(2.4)=1.25
α=1.25

so assuming θ₀=0

θ=-9(2.4)+1/2(1.25)(2.4)²
θ=-18?

Your calculated angular acceleration is wrong. The angular velocity at time zero is -9 rad/s, and it is zero at time 6 seconds. So it increases by 9 rad/s over a time interval of 6 seconds.

 

[SalsaOnMyTaco]

Your calculated angular acceleration is wrong. The angular velocity at time zero is -9 rad/s, and it is zero at time 6 seconds. So it increases by 9 rad/s over a time interval of 6 seconds.

Thanks,
but shouldn't my final angular velocity be -6 since its asking for the displacemente at 2.4s?

 

[azizlwl]

Thanks,
but shouldn't my final angular velocity be -6 since its asking for the displacemente at 2.4s?

It is a constant acceleration. Which means Δv/Δt is constant. You can take any points as values.
The problem is that you are taking velocity at time of 2.4 secs.
You can only get approximate value of v at 2.4 sec from the graph.

Rather than taking value of velocity at 2.4sec, why not use other values that easy and accurate to calculate. It does not matter where you get your Δv and Δt since it is a linear function.