Direction of angular acceleration

In summary, the angular acceleration of the wheels in this scenario is in the +x-direction. This is because the wheels have an angular velocity in the -x-direction and decreasing this velocity requires a force in the opposite direction, which would be in the +x-direction. The problem may have been poorly phrased, but thinking about it in terms of applying a force to stop the wheels can help with understanding the solution.
  • #1
brendan3eb
54
0

Homework Statement


Imagine a car driving on the XY plane in the +y-direction. If it is slowing down, in what direction is the angular acceleration of the wheels?

(a) the +x-direction
(b) the -x-direction
(c) the +y-direction
(d) the -y-direction
(e) the +z-direction

Homework Equations


a=αR

The Attempt at a Solution


I am just really lost when it comes to this problem. The apparent answer is A, but I do not understand why. I can't conceptualize angular acceleration with the axes..

The solution says the wheels have an angular velocity in the -x-direction and thus since the angular velocity is decreased the acceleration would be in the +x-direction. I get the second step, but I don't understand how you determine the angular velocity is in the -x-direction
 
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  • #2
Actually, I think I get it now after messing around with some pictures..still, I think this was a stupid and poorly phrased problem.
 
  • #3
think it as applying a force to stop the wheels...
 

FAQ: Direction of angular acceleration

What is angular acceleration?

Angular acceleration is the rate of change of angular velocity, which is the speed at which an object rotates or moves around a fixed point. It is a vector quantity, meaning it has both magnitude and direction.

What is the equation for angular acceleration?

The equation for 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.

How is angular acceleration different from linear acceleration?

Angular acceleration refers to the change in rotational motion, while linear acceleration refers to the change in straight-line motion. Angular acceleration is measured in radians per second squared, while linear acceleration is measured in meters per second squared.

What factors affect the direction of angular acceleration?

The direction of angular acceleration is affected by the direction of the torque applied to an object, as well as the direction of the object's moment of inertia. The direction of motion of the object also plays a role in determining the direction of angular acceleration.

How is angular acceleration related to angular velocity?

Angular acceleration and angular velocity are directly related, as angular acceleration is the rate of change of angular velocity. If the angular acceleration is constant, the angular velocity will increase or decrease at a steady rate. Conversely, a changing angular acceleration will result in a changing angular velocity.

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