Angular Acceleration vector help

In summary, the problem asks for the magnitude of the average angular acceleration and the angle it makes with the horizontal axis. To solve this, begin by expressing the initial conditions in terms of angular velocity vectors and then find the net change in velocity over the given time period. This will give you the average acceleration vector, from which you can find the magnitude and angle. Paying attention to units is important in solving the problem and identifying any errors.
  • #1
skinnbones
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Im a fairly new to physics and I have a homework question off mastering physics which is , A wheel is spinning at 43rpm with its axis vertical. After 15 sec , it's spinning at 61rpm with its axis horizontal. Find (a) the magnitude of its average angular acceleration and (b) the angle the average angular acceleration vector makes with the horizontal.

Part A
Express your answer using two significant figures.
alpha= _____ rad/s^2

Part B
Theta=_____°

Im not quite sure how to do it and was wondering if someone could please help and explain the process of how to answer the question. I know you're not meant to do this but I honestly want to understand it, I just don't know how begin
 
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  • #2
For starters let's pay attention to units. "After 15, "15 what? turns? Days? ... It isn't just a matter of being uptight about details. Watching the units gives you a guide to solving the problem and as importantly to identifying when and where you've made an error.

That having been said, I'll begin with some guidelines. The form of the problem implies you should work in a vector format. So express your initial conditions in terms of formal vectors. (i.e. angular velocity vectors.)

Now don't focus too much on the "angular" part but on the general idea. You have a change in some kind of velocity over some period of time. Acceleration is the rate of change of velocity so average acceleration is a net change in velocity over a net change in time. Net change is difference an so you can still talk about net change in vector format since you can add and subtract vectors.

So find the average acceleration vector and then answer the appropriate questions about it.
 

1. What is angular acceleration?

Angular acceleration is a vector quantity that measures the rate of change of angular velocity with respect to time. It is the change in angular velocity per unit time and is typically denoted by the symbol alpha (α).

2. How is angular acceleration calculated?

Angular acceleration can be calculated by taking the derivative of angular velocity with respect to time, or by dividing the change in angular velocity by the change in time. It is measured in units of radians per second squared (rad/s2).

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

Linear acceleration is the rate of change of an object's linear velocity, while angular acceleration is the rate of change of an object's angular velocity. Linear acceleration is a scalar quantity, while angular acceleration is a vector quantity.

4. How does angular acceleration affect rotational motion?

Angular acceleration plays a crucial role in rotational motion as it determines how quickly an object is rotating and how much torque is being applied. It is directly proportional to the net torque acting on an object and is responsible for causing changes in an object's angular velocity and direction of rotation.

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

Some common examples of angular acceleration include the motion of a Ferris wheel, the rotation of a spinning top, and the movement of a car around a curved track. Other examples can be seen in sports, such as a pitcher throwing a curveball or a figure skater performing a spin.

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