# Angular acceleration and velocities - verification of work

• gate13
In summary, the conversation discusses a problem involving angular acceleration and velocities. The individual has attached a pdf with their worked out solution and is seeking feedback on its accuracy. There is a question about total acceleration at a certain point in time that is unclear and another question involving circular and vertical motion.
gate13
Good day to all.

I have worked out a problem concerning angular acceleration and velocities but I am not sure if what I have done is correct. I have attached all the worked out problem as a pdf as I wanted it to be as clear and concise as possible, especially when someone is taking time from their schedule to answer my question. I hope the question and solutions provided are clear.

Again, once again any feedback would be greatly appreciated.

#### Attachments

• Angular_problem.pdf
290.3 KB · Views: 316
all your answers look good to me. And your reasoning for part g) looks good as well.

The question for part e) is hard to understand, because after 7 seconds, there is no tangential acceleration. And before 7 seconds, there is tangential acceleration. It asks about the total acceleration at 7 seconds, so it is not obvious if we are to assume that there is (or isn't) any tangential acceleration. You see what I mean?

Part g) is a bit complicated as well. I'm guessing that thing is simply attaching wheels 2 and 3, so that wheel 3 will move in circular motion around the centre of wheel 2. And the question asks for vertical motion, so you're probably going to need to figure out circular motion then work out vertical motion.

## 1. What is angular acceleration?

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

## 2. How is angular acceleration calculated?

Angular acceleration (α) can be calculated by dividing the change in angular velocity (Δω) by the change in time (Δt), using the formula α = (Δω/Δt).

## 3. What is the difference between angular acceleration and linear acceleration?

Angular acceleration refers to the change in rotational speed of an object, while linear acceleration refers to the change in linear speed (velocity) of an object. Angular acceleration is measured in radians per second squared (rad/s^2), while linear acceleration is measured in meters per second squared (m/s^2).

## 4. How is angular velocity verified?

Angular velocity can be verified by using a device called an accelerometer, which measures the rate of change of angular velocity. This data can then be compared to the calculated angular velocity using the formula ω = 2π/T, where T is the period of rotation.

## 5. What is the relationship between angular acceleration and work?

The relationship between angular acceleration and work is similar to that of linear acceleration and work. Work (W) is equal to the product of force (F) and displacement (s), or W = Fs. In the case of angular acceleration, the force is the torque (τ) applied to an object and the displacement is the angle (θ) through which the object rotates. Therefore, work can be calculated using the formula W = τθ.

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