Calculate Angular Displacement: 2.1rad/s to 0rad/s in 4.7s

In summary, to find the angular displacement of a fan rotating at 2.1 radian/s with a constant acceleration and coming to a stop in 4.7 seconds, you would use the equation \Delta\theta=\omega_{i}t+\frac{1}{2}\alpha t^2 and find \alpha using the equation \omega_{f}=\omega_{i}+\alpha t.
  • #1
tica86
79
0
A fan rotating at 2.1 radian/s slows down with a constant acceleration and comes to a stop in a time of 4.7 s. What is its angular displacement in this time?

Is this what I'm supposed to use: Δθ = Δθ2 − Δθ1?

if it is I'm not sure how to begin to solve this problem, if anyone could help me out, thanks!
 
Physics news on Phys.org
  • #2
For the case of constant acceleration, you need to use

[tex]\delta\theta=\omega_{i}t+\frac{1}{2}\alpha t^2[/tex]

find alpha from

[tex]\omega_{f}=\omega_{i}+\alpha t[/tex]

you have been given initial and final angular velocities
 
  • #3
For the case of constant acceleration, you need to use

[tex]\Delta\theta=\omega_{i}t+\frac{1}{2}\alpha t^2[/tex]

find alpha from

[tex]\omega_{f}=\omega_{i}+\alpha t[/tex]

you have been given initial and final angular velocities
 
  • #4
IssacNewton said:
For the case of constant acceleration, you need to use

[tex]\Delta\theta=\omega_{i}t+\frac{1}{2}\alpha t^2[/tex]

find alpha from

[tex]\omega_{f}=\omega_{i}+\alpha t[/tex]

you have been given initial and final angular velocities

Ok, I tried the following and I know it's wrong but I'm really lost:

=2.1*10+1/2*.4468

.4468(2.1/4.7)
 
  • #5
Initial angular velocity [itex]\omega_i= 2.1 \, rad/sec [/itex] and since the stuff comes to rest, final angular velocity [itex]\omega_f=0 [/itex] and the time t is given. With this information , can you find the [itex]\alpha[/itex] using one of the equations I have given ?
 

1. What is angular displacement?

Angular displacement is the change in the angle or rotation of an object over time.

2. How do you calculate angular displacement?

To calculate angular displacement, you need to know the initial angular velocity, final angular velocity, and time interval. The formula for angular displacement is: θ = ωit + 1/2αt2, where θ is the angular displacement, ωi is the initial angular velocity, t is the time interval, and α is the angular acceleration (assuming it is constant).

3. What is the unit of angular displacement?

The unit of angular displacement is in radians (rad) or degrees (°). In this case, the angular displacement is in radians.

4. How do you convert from radians per second to radians per second squared?

To convert from radians per second to radians per second squared, you need to divide the change in angular velocity by the change in time. In this example, the change in angular velocity is 2.1rad/s - 0rad/s = 2.1rad/s, and the change in time is 4.7s, so the angular acceleration would be 2.1rad/s ÷ 4.7s = 0.447rad/s2.

5. Can you explain the concept of angular acceleration?

Angular acceleration is the rate of change of angular velocity over time. It is similar to how linear acceleration is the rate of change of linear velocity over time. If an object is rotating with a constant angular acceleration, its angular velocity will increase or decrease at a steady rate. This can be calculated using the formula α = (ωf - ωi) ÷ t, where α is the angular acceleration, ωf is the final angular velocity, ωi is the initial angular velocity, and t is the time interval.

Similar threads

  • Introductory Physics Homework Help
2
Replies
54
Views
2K
  • Introductory Physics Homework Help
Replies
7
Views
197
  • Introductory Physics Homework Help
Replies
2
Views
2K
  • Introductory Physics Homework Help
Replies
2
Views
1K
  • Introductory Physics Homework Help
Replies
10
Views
2K
  • Introductory Physics Homework Help
Replies
2
Views
1K
  • Introductory Physics Homework Help
Replies
1
Views
2K
  • Classical Physics
2
Replies
61
Views
853
  • Introductory Physics Homework Help
Replies
4
Views
1K
  • Introductory Physics Homework Help
Replies
3
Views
1K
Back
Top