contestada

A rotating wheel has a constant angular acceleration. It has an angular velocity of 5.0 rad/s at time t = 0 s, and 3.0 s later has an angular velocity of 9.0 rad/s. What is the angular displacement of the wheel during the 3.0-s interval?

Respuesta :

Angular displacement during 3 seconds is 21 rad

Explanation:

We have equation of motion v = u + at

     Initial velocity, u = 5 rad/s

     Final velocity, v = 9 rad/s    

     Time, t = 3 s

     Substituting

                      v = u + at  

                      9 = 5 + a x 3

                      a = 1.33 rad/s²

     Angular acceleration is 1.33 rad/s²

Now we have equation of motion v² = u² + 2as

     Initial velocity, u = 5 rad/s

     Final velocity, v = 9 rad/s    

     Angular acceleration = 1.33 rad/s²

Substituting  

v² = u² + 2as

9² = 5² + 2 x 1.33 x s

s = 21 radians

Angular displacement during 3 seconds is 21 rad

asuwafohjames

The angular displacement of the wheel during the 3.0-s interval is 6 rad.

To calculate the angular displacement of the wheel, we use the formula below

Formula:

  • θ = (ω₁+ω₂)t/2............... Equation 1

Where:

  • θ = angular displacement of the wheel
  • ω₁ = Initial angular velocity
  • ω₂ = Final angular velocity
  • t = time.

From the question,

Given:

  • ω₁ = 5 rad/s
  • ω₂ = 9 rad/s
  • t = 3 s

Substitute these values into equation 1

  • θ  = (9-5)3/2
  • θ  = (4×3)/2
  • θ  = 6 rad.

Hence, The angular displacement of the wheel during the 3.0-s interval is 6 rad.

Learn more about angular displacement here: https://brainly.com/question/24882338

Otras preguntas