Calculus angular acceleration with respect to theta

In summary, a disk with a 0.4 m radius has an angular acceleration of α = (10θ2/3)rad/s2, where θ is in radians. When t = 4s, the magnitude of the normal (centripetal and tangential components of a point P on the rim of the disk can be found by using the equations α = dω/dt, ω = dθ/dt, Vt = ω * r, and ac = Vt2/r. The solution involves finding ω in terms of θ and using a separable differential equation to solve for θ. However, some teachers may not consider this method to be conventional or "legal" math.
  • #1
nick76342
7
0

Homework Statement


A disk with a 0.4 m radius starts from rest and is given an angular acceleration α = (10θ2/3)rad/s2 , where θ is in radians. Determine the magnitude of the normal (centripetal and tangential components of a point P on the rim of the disk when t = 4s.

Homework Equations


α = dω/dt
ω = dθ/dt
Vt = ω * r
ac = Vt2/r

The Attempt at a Solution


I have been successful in finding ω, but only in terms of θ. Our teacher has showed us a method by which we use the ω = dθ/dt equation to find θ, however the method that he used involved dividing θ through anti-derivatives. I am not sure how this works in terms of legal math. I see that this problem exists elsewhere so what is the conventional way of solving? My calculus II teacher was not pleased with my physic's teachers method of solving. Any ideas? I am able to solve for everything else in this problem, I just need to find theta from the equation I derived (which I know is correct) ω = (√(15) * θ2/3)rad/s.Thanks.
 
Physics news on Phys.org
  • #2
You know that ##\omega = d\theta/dt##. Inserting this into your expression gives yoy a separable differential equation.
 
  • #3
nick76342 said:

Homework Statement


A disk with a 0.4 m radius starts from rest and is given an angular acceleration α = (10θ2/3)rad/s2 , where θ is in radians. Determine the magnitude of the normal (centripetal and tangential components of a point P on the rim of the disk when t = 4s.

Homework Equations


α = dω/dt
ω = dθ/dt
Vt = ω * r
ac = Vt2/r

The Attempt at a Solution


I have been successful in finding ω, but only in terms of θ. Our teacher has showed us a method by which we use the ω = dθ/dt equation to find θ, however the method that he used involved dividing θ through anti-derivatives. I am not sure how this works in terms of legal math. I see that this problem exists elsewhere so what is the conventional way of solving? My calculus II teacher was not pleased with my physic's teachers method of solving. Any ideas? I am able to solve for everything else in this problem, I just need to find theta from the equation I derived (which I know is correct) ω = (√(15) * θ2/3)rad/s.Thanks.
You marked the problem as solved. Can you show us your solution?
 

FAQ: Calculus angular acceleration with respect to theta

1. What is calculus angular acceleration with respect to theta?

Calculus angular acceleration with respect to theta is a mathematical concept used to measure the rate of change of angular velocity with respect to the angle theta. It is commonly used in physics and engineering to analyze rotational motion.

2. How is angular acceleration calculated using calculus?

Angular acceleration is calculated by taking the derivative of angular velocity with respect to time. In other words, it is the change in angular velocity divided by the change in time. This can also be represented as the second derivative of the angle theta with respect to time.

3. What does a positive angular acceleration indicate?

A positive angular acceleration indicates that the angular velocity is increasing, meaning that the object is rotating in the direction of increasing angle theta. This can happen if there is a constant torque applied to the object or if the moment of inertia decreases.

4. How does angular acceleration differ from linear acceleration?

Angular acceleration and linear acceleration are both measures of how quickly an object is changing its velocity. However, angular acceleration measures the change in angular velocity while linear acceleration measures the change in linear velocity. Additionally, angular acceleration is a vector quantity while linear acceleration is a scalar quantity.

5. What are some real-world applications of calculus angular acceleration with respect to theta?

Calculus angular acceleration with respect to theta is used in many real-world applications such as analyzing the motion of rotating machinery, understanding the dynamics of planets and satellites in orbit, and designing roller coasters and other amusement park rides. It is also used in sports such as figure skating and gymnastics to analyze the rotational motion of athletes.

Similar threads

What is the angle between the acceleration and velocity when rotating?
Replies
13
Views
2K
Position vector for anti-clockwise circular motion derivation
Replies
5
Views
978
Angular Position, Speed, and Acceleration of a Swinging Door at t=0s and t=3.10s
Replies
15
Views
2K
Angular Velocity and Acceleration
Replies
3
Views
2K
Angular Velocity and Acceleration graph
Replies
4
Views
6K
Angular Velocity and Acceleration
Replies
10
Views
2K
What is the net acceleration of the coin on a rotating disk?
Replies
2
Views
2K
Rotational Motion: Average angular acceleration of a CD
Replies
2
Views
5K
Acceleration around a running track
Replies
3
Views
3K
Angular Acceleration (Grindstone Problem)
Replies
5
Views
3K

Hot Threads

Recent Insights

Back
Top