How to find angular acceleration

In summary, The propeller has an average angular acceleration of -62.9 rad/s^2. The variables in the relevant equations refer to angular acceleration (ac), velocity (v), radius (r), and angular velocity (w).
  • #1
itsmarasilly
24
0

Homework Statement


A propeller slows from 450 rev/min to 200 rev/min in 3.50 s. What is its angular acceleration?

Homework Equations


ac = v^2/r
and v = rw

The Attempt at a Solution


I know this is probably a simple problem, but what do the variables in the relevant equations refer to?
 
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  • #2
itsmarasilly said:

Homework Statement


A propeller slows from 450 rev/min to 200 rev/min in 3.50 s. What is its angular acceleration?

Homework Equations


ac = v^2/r
and v = rw

The Attempt at a Solution


I know this is probably a simple problem, but what do the variables in the relevant equations refer to?

Here are some more relevant equations:

[tex]\frac{1 rev}{min}=\frac{1 rev}{60 s}=\frac{\pi rad}{30 s}[/tex], and
[tex]\vec{\alpha}_{ave}=\frac{\Delta\vec{\omega}}{\Delta t}[/tex].
 
  • #3



To find the angular acceleration of the propeller, we can use the equation ac = v^2/r, where ac is the angular acceleration, v is the linear velocity, and r is the radius of the propeller. In this case, we are given the initial and final angular velocities, 450 rev/min and 200 rev/min respectively, and the time interval of 3.50 s.

Using the equation v = rw, we can calculate the linear velocity at each time point by multiplying the angular velocity by the radius of the propeller. This will give us an initial velocity of 235.62 m/s and a final velocity of 104.72 m/s.

Plugging these values into the equation ac = (vf^2 - vi^2)/r, we get an angular acceleration of -9.65 rad/s^2. The negative sign indicates that the propeller is experiencing a deceleration, which is expected since it is slowing down from 450 rev/min to 200 rev/min.

In summary, the angular acceleration of the propeller is -9.65 rad/s^2.
 

1. What is angular acceleration?

Angular acceleration is a measure of how quickly an object's angular velocity changes over time. It is a vector quantity, meaning it has both magnitude and direction.

2. How is angular acceleration different from linear acceleration?

Angular acceleration is a measure of how quickly an object's rotational speed changes, while linear acceleration is a measure of how quickly an object's linear velocity changes. In other words, angular acceleration refers to changes in the direction or magnitude of an object's rotational motion, while linear acceleration refers to changes in the direction or magnitude of an object's linear motion.

3. How do you calculate angular acceleration?

Angular acceleration can be calculated by dividing the change in angular velocity by the change in time. The formula for angular acceleration is: α = (ω2 - ω1) / (t2 - t1), where α is angular acceleration, ω2 and ω1 are the final and initial angular velocities, and t2 and t1 are the final and initial times.

4. What is the unit of measurement for angular acceleration?

The unit of measurement for angular acceleration is radians per second squared (rad/s2). This unit can also be written as rad s-2.

5. How can I find the angular acceleration of an object in real life?

To find the angular acceleration of an object in real life, you will need to measure the change in angular velocity over a certain amount of time. This can be done using tools such as a tachometer or by recording and analyzing video footage of the object's motion. Once you have these measurements, you can use the formula mentioned in question 3 to calculate the angular acceleration.

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