Angular Acceleration of a Moving Wheel

In summary, the problem is asking for the angular acceleration of a cyclist's wheels after 4.6 seconds of pedaling, given that they have made 8.5 revolutions. The correct equation to use is w^2 = wi^2 + 2a(theta), but it is important to note that the initial angular velocity may not always be 0.
  • #1
underoathP
5
0
I am having a bit of trouble with the following problem.

A cyclist starts from rest and pedals so that the wheels make 8.5 revolutions in the first 4.6 s. What is the angular acceleration of the wheels (assumed constant)?

I multiplied 8.5 by 2pi and then divided by 4.6 sec. I get an answer of 11.6 rad/sec, but they want an answer in rad/sec^2. Am I doing this right?
 
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  • #2
underoathP said:
I am having a bit of trouble with the following problem.

A cyclist starts from rest and pedals so that the wheels make 8.5 revolutions in the first 4.6 s. What is the angular acceleration of the wheels (assumed constant)?

I multiplied 8.5 by 2pi and then divided by 4.6 sec. I get an answer of 11.6 rad/sec, but they want an answer in rad/sec^2. Am I doing this right?
I see you've found the Homework Forums, :wink:.

Not quite. What is the definition of angular acceleration?
 
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  • #3
Angular Acceleration

The definition of angular acceleration is angular velocity over time. So, to get angular velocity from 8.5 rev/4.6 sec you have to find the angular velocity first. So, the definition of angular velocity (omega) is angular displacement over time, and the angular displacement is in radians. That is why I multiplied 8.5 by 2pi. Do I have to divide by 4.6 again?
 
  • #5
I looked at that website and this is what makes sense to me:

8.5 rev * 2pi = 53.41 radians
53.41 rad / 4.6 sec = 11.61 rad/sec (omega)
11.61 rad/sec / sec = 2.5 rad/sec^2

2.5 is the wrong answer when I entered it. I am out of ideas.
 
  • #6
underoathP said:
I looked at that website and this is what makes sense to me:

8.5 rev * 2pi = 53.41 radians
53.41 rad / 4.6 sec = 11.61 rad/sec (omega)
11.61 rad/sec / sec = 2.5 rad/sec^2

2.5 is the wrong answer when I entered it. I am out of ideas.
Okay, how about this section of the website;

drot2.gif


Which equation do you suppose would be appropriate in this case?
 
  • #7
wait what happened to this? was there an answer discussed? I am so confused! i have a very similar problem and I am doing the same thing.

I think the right equation is w^2= wi^2+2a(theta)

but i used that assuming the initial angular velocity is 0 and its wrong
 

FAQ: Angular Acceleration of a Moving Wheel

What is angular acceleration?

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

How is angular acceleration calculated?

Angular acceleration can be calculated by dividing the change in angular velocity by the change in time. It is represented by the symbol alpha (α) and has the unit of radians per second squared (rad/s²).

What is the difference between linear and angular acceleration?

Linear acceleration refers to the change in velocity of an object in a straight line, while angular acceleration refers to the change in rotational speed of an object around an axis. They have different units of measurement and represent different types of motion.

How does the angular acceleration of a moving wheel affect its motion?

The angular acceleration of a moving wheel determines how quickly the wheel's rotational speed changes. A higher angular acceleration means the wheel will speed up or slow down more quickly, while a lower angular acceleration means the wheel will change speed more gradually.

What factors can affect the angular acceleration of a moving wheel?

The angular acceleration of a moving wheel can be affected by the applied torque (force) on the wheel, the moment of inertia (resistance to rotation) of the wheel, and any external forces acting on the wheel. The shape and size of the wheel can also impact its angular acceleration.

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