Angular Acceleration: Find Angle in 2 Seconds

In summary, angular acceleration is the rate of change of angular velocity over time and can be calculated using the formula α = (ω<sub>2</sub> - ω<sub>1</sub>) / t. It is typically measured in radians per second squared (rad/s<sup>2</sup>), but can also be expressed in degrees per second squared (deg/s<sup>2</sup>). Angular acceleration and linear acceleration are related through the distance from the axis of rotation, and to find the angle in 2 seconds, you can use the formula θ = ω<sub>0</sub>t + 1/2αt<sup>2</sup>.
  • #1
omgitsmonica
22
0

Homework Statement


A wheel accelerates with constant angular acceleration of 6 rad/22. If the initial angular velocity is 6 rad/s. what is the angle in degrees that the wheel rotates through in 2 seconds?


Homework Equations



360 degrees = 2pi radians

The Attempt at a Solution



6*2pi = 37.699

Can it really be that simple?
 
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  • #2
No. For one thing, the wheel is accelerating. That is important, you can't just ignore it. Make a list of what you know, and apply the appropriate equation to find what you don't know.
 
  • #3


Yes, it can be that simple! The formula for angular displacement is θ = ω0t + 1/2αt^2, where θ is the angular displacement, ω0 is the initial angular velocity, α is the angular acceleration, and t is the time. Plugging in the given values, we get θ = (6 rad/s)(2 s) + 1/2(6 rad/s^2)(2 s)^2 = 12 rad = 12(360 degrees/2pi radians) ≈ 684.24 degrees. So, in 2 seconds, the wheel rotates approximately 684.24 degrees.
 

1. What is angular acceleration?

Angular acceleration is the rate of change of angular velocity over time. It is a measure of how quickly an object's angular velocity (rotational speed) is changing.

2. How do you calculate angular acceleration?

Angular acceleration can be calculated using the formula α = (ω2 - ω1) / t, where α is angular acceleration, ω2 is the final angular velocity, ω1 is the initial angular velocity, and t is the time interval.

3. What units is angular acceleration measured in?

Angular acceleration is typically measured in radians per second squared (rad/s2). However, it can also be expressed in degrees per second squared (deg/s2).

4. How does angular acceleration relate to linear acceleration?

Angular acceleration and linear acceleration are related through the distance from the axis of rotation. The further away an object is from the axis of rotation, the greater its linear acceleration will be for a given angular acceleration.

5. How do I find the angle in 2 seconds using angular acceleration?

To find the angle in 2 seconds, you will need to know the initial angular velocity and the angular acceleration. Use the formula θ = ω0t + 1/2αt2, where θ is the angle, ω0 is the initial angular velocity, α is the angular acceleration, and t is the time interval (in this case, 2 seconds).

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