Angular Acceleration of Wheels: Solve Homework Problem

In summary, angular acceleration is the rate of change of angular velocity over time and is a measure of how quickly the rotational speed of an object is changing. It differs from linear acceleration in that it refers to changes in rotational speed rather than linear velocity. Angular acceleration and torque are directly proportional, and it can be calculated by dividing the change in angular velocity by the change in time. In engineering, understanding angular acceleration is crucial for designing and optimizing mechanical systems that involve rotational motion, such as wheels, engines, and gears.
  • #1
Devin Longo
11
0

Homework Statement



A cyclist starts from rest and pedals so that the wheels make 8.5 revolutions in the first 4.5 s. What is the angular acceleration of the wheels (assumed constant)?



Homework Equations



[tex]\alpha[/tex] = [tex]\Delta[/tex][tex]\omega[/tex]/ [tex]\Delta[/tex]t



The Attempt at a Solution



I converted 8.5 to radians and divided by 4.5. BUT I CANT GET THE RIGHT ANSWER!
 
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  • #2
Use the formula
θ = ωο*t + 1/2*α*t^2 and find α.
 
  • #3
So, I do that and I get .839. I kept 8.5 as my theta. It still isn't right. What could I be doing wrong?
 
  • #4
No. The angular displacement θ = 2*π*n, where n is the number of revolutions per second.
 

1. What is angular acceleration?

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

2. How is angular acceleration different from linear acceleration?

Angular acceleration refers to the change in rotational speed, while linear acceleration refers to the change in linear velocity. Angular acceleration is measured in radians per second squared, while linear acceleration is measured in meters per second squared.

3. How is angular acceleration related to torque?

Angular acceleration and torque are directly proportional. The greater the torque applied to an object, the greater its angular acceleration will be.

4. How can I calculate angular acceleration?

Angular acceleration can be calculated by dividing the change in angular velocity by the change in time. This can be represented by the formula α = Δω / Δt, where α is the angular acceleration, Δω is the change in angular velocity, and Δt is the change in time.

5. How is angular acceleration of wheels important in engineering?

Angular acceleration of wheels is important in engineering because it is crucial for understanding the rotational motion of objects, such as wheels. It is also essential for designing and optimizing various mechanical systems, such as engines and gears, that involve rotational motion.

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