# Explanation needed in angular acceleration

• Schwatt!
In summary, the problem involves a disk rotating with constant angular acceleration and the question asks for the magnitude of the angular acceleration, the average angular velocity, the instantaneous angular velocity at the end of 5.0 s, and the additional angle the disk will turn in the next 5.0 s. The formula used to solve this problem is θ = ω0t + 1/2αt^2 and the value to be used for θ is the given 25 rad, which corresponds to the angular displacement after 5.0 s. The correct quantity to plug in for the angular velocity is 25/5, which gives an angular velocity of 5 rad/s.
Schwatt!
Hi all, I am doing some homework from my textbook and I encountered this problem:

"Starting from rest, a disk rotates about its central axis with constant angular acceleration. In 5.0 s, it rotates 25 rad. During that time, what are the magnitudes of (a) the angular acceleration and (b) the average angular velocity? (c) Wha is the instantaneous angular velocity of the disk at the end of the 5.0 s? (d) With the angular acceleration unchanged, through what additional angle will the disk turn during the next 5.0s?"

I have a problem calculating the value for (a). I have the answer but I am not sure why I am right. Using θ = ω0t+ 1/2αt^2 and solving for a, what is the value to be used for θ? Would it be the given 25 rad. or 25 rad/5 s?

$\theta$ is an angle, not an angular velocity.

If all else fails, use unit analysis to check what you should plug in.

ok so that would mean to plug in the radian measure but that number does not give the answer; the 25/5 does...

Schwatt! said:
ok so that would mean to plug in the radian measure but that number does not give the answer; the 25/5 does...
The 25/5 is the correct quantity, that is what Saketh was hinting at. Since;

$$\omega=\frac{d\theta}{dt} = \frac{25}{5} = 5\;rad.s^{-1}$$

## 1. What is angular acceleration?

Angular acceleration is a measure of the rate at which an object's angular velocity changes over time. It is represented by the symbol alpha (α) and is measured in radians per second squared (rad/s²).

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

Angular acceleration and linear acceleration are both measures of how an object's velocity changes over time. However, angular acceleration specifically refers to the change in an object's rotational velocity, while linear acceleration refers to the change in its linear velocity.

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

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

## 4. How is angular acceleration related to torque?

Angular acceleration is directly proportional to the torque applied to an object. This means that the greater the torque, the greater the object's angular acceleration will be. This relationship is described by the formula α = τ / I, where τ is the torque and I is the moment of inertia of the object.

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

Angular acceleration can be observed in many everyday situations, such as when a car turns a corner, a spinning top slows down and falls over, or a figure skater spins faster by pulling in their arms. It is also important in engineering and design, such as in the rotation of propellers on a plane or the rotation of gears in a machine.

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