Uniform angular acceleration

In summary, a wheel with uniform angular acceleration starting from rest rotates 90.6 degrees in the first 1-second time interval. To find the angle it rotates during the next 1-second time interval, you can use rotational versions of equations for constant acceleration, such as d=1/2at^2+Vi*t, with distance in radians, angular velocity in radians/second, and acceleration in radians/s^2. For the third 1-second time interval, the angle will increase in smaller increments due to the wheel's increasing speed. To convert from revolutions per minute to radians/second, divide by 60 and multiply by 2*Pi.
  • #1

Homework Statement

A wheel is subjected to uniform angular acceleration. Initially its angular velocity is zero. During the first 1-s time interval, it rotates through an angle of 90.6degrees.

(a) Through what angle does it rotate during the next 1-s time interval?(in degrees)

(b) Through what angle during the third 1-s time interval?(in degrees)

Homework Equations


The Attempt at a Solution

I just tried multiplying the 90.6 by 2, and putting in 90.6 itself, because I thought that might be the answer, but I forgot that it was the acceleration, and that the next values would increase in smaller increments, because it is speeding up.
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  • #2
You can use all your equations you've been using for constant acceleration, like d=1/2at^2+Vi*t, but now you use the rotational "versions"

so instead of distance in meters, you have the angle traveled in radians, instead of velocity in meters/second, angular velocity in radians/second, and acceleration is radians/s^2

So in one second it goes from 0 degrees to 90.6 starting from rest(you'll need radians!)this is like knowing distance, time, and initial velocity
  • #3
Okay, so since I have 5400 rev/min, I divide it by 60 to get 90 rev/sec. Then I multiply it by 2*Pi for the angular velocity in radians, right? Or am I doing something wrong?
  • #4
That part's right

except the unit is radians/second
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1. What is uniform angular acceleration?

Uniform angular acceleration is the rate at which the angular velocity of an object changes in a uniform manner. It is the change in angular velocity divided by the change in time.

2. How is uniform angular acceleration different from linear acceleration?

Uniform angular acceleration refers to the change in rotational speed, while linear acceleration refers to the change in linear speed. They are different because rotational motion involves a circular path, while linear motion involves a straight path.

3. What is the formula for calculating uniform angular acceleration?

The formula for uniform angular acceleration is α = (ωf - ωi) / t, where α is the angular acceleration, ωf is the final angular velocity, ωi is the initial angular velocity, and t is the time interval.

4. How is angular velocity related to uniform angular acceleration?

Angular velocity and uniform angular acceleration are directly related. The change in angular velocity is equal to the product of the uniform angular acceleration and the change in time, or ωf - ωi = αt. This means that as the angular acceleration increases, the angular velocity also increases.

5. What are some real-life examples of uniform angular acceleration?

Some examples of uniform angular acceleration include the spinning of a top, the rotation of a carousel, and the motion of a Ferris wheel. These objects all have a constant increase or decrease in angular velocity, resulting in uniform angular acceleration.

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