Figuring out angular velocity from θ = 2.0 + 4.0t^2 + 2.0t^3

In summary, the conversation discusses the angular position, velocity, and acceleration of a point on a rotating wheel, with the given equation θ = 2.0 + 4.0t2 + 2.0t3. The question asks for the angular position and velocity at t = 0, the angular velocity at t = 4.0 s, and the angular acceleration at t = 2.0 s. The equation for angular velocity is w = (8.0rad/s^2)t + (6.0rad/s^3)t^2, and it is mentioned that the angular acceleration may not be constant.
  • #1
Stonem42
1
0

Homework Statement



The angular position of a point on a rotating wheel is given by θ = 2.0 + 4.0t2 + 2.0t3, where θ is in radians and t is in seconds. At t = 0, what are (a) the point's angular position and (b) its angular velocity? (c) What is its angular velocity at t = 4.0 s? (d) Calculate its angular acceleration at t = 2.0 s. (e) Is its angular acceleration constant?

Homework Equations



w = dθ/dt I am stuck on figuring out how to angular velolcity is:

(8.0rad/s^2)t + (6.0rad/s^3)t^2

as my professor put it, its buggin me how i can't put two and two together.

The Attempt at a Solution

 
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  • #2
Stonem42 said:
w = dθ/dt I am stuck on figuring out how to angular velolcity is:

I'm stuck on what you're stuck on. What?
 

1. What is angular velocity?

Angular velocity is the rate of change of an object's angular displacement over time. It is measured in radians per second (rad/s) or degrees per second (°/s).

2. How do you calculate angular velocity?

Angular velocity can be calculated by dividing the change in angular displacement by the change in time. It can also be found by taking the derivative of the angular displacement equation with respect to time.

3. What does θ = 2.0 + 4.0t^2 + 2.0t^3 represent?

This equation represents the angular displacement of an object at a given time, t. The first term (2.0) represents the initial angular displacement, while the second term (4.0t^2) and third term (2.0t^3) represent the angular displacement due to linear acceleration and angular acceleration, respectively.

4. How can you use θ = 2.0 + 4.0t^2 + 2.0t^3 to find the angular velocity?

To find the angular velocity, you can take the derivative of the equation with respect to time. This will give you an equation for angular velocity, which can then be calculated at a specific time by plugging in the value of t.

5. Can the equation θ = 2.0 + 4.0t^2 + 2.0t^3 be used for any object's angular displacement?

No, this equation is specific to an object with linear and angular acceleration. It cannot be used for objects with constant angular velocity or objects that do not experience acceleration.

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