What is the angular acceleration of an arm

In summary, the question is asking for the angular acceleration of an arm at theta=45 degrees, with a velocity of 2 m/s and a picture attached. The solution involves using the law of sines to find the length of side r, and then taking the time derivative of theta using either the law of cosine or sine. The hint suggests using a vector expression to solve for the angular orientation of the arm, and then taking the time derivative of that result.
  • #1
Dusty912
149
1

Homework Statement


what is the angular acceleration of the arm when theta equals 45 degrees.
v=2 m/s
picture is attached

Homework Equations


law of sites
law of cosines

The Attempt at a Solution


[/B]
so I used the law of sines to resolve side r as being 579.555 mm
now I now I need to take time derivative of theta somewhere using law of cosine or sines but I'm not really sure which one. also I don't know how to relate the 2 m/s to the problem
 

Attachments

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  • #2
Hint: The velocity is telling you how fast the long side is increasing.
 
  • #3
Write the vector expression describing the closed loop. Solve this for the angular orientation of the arm (it will appear in the vector components). Take the time derivative of that result.
 

Related to What is the angular acceleration of an arm

1. What is angular acceleration?

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

2. How is angular acceleration calculated?

Angular acceleration is calculated by dividing the change in angular velocity by the change in time. The formula for angular acceleration is a = Δω/Δt, where a is angular acceleration, Δω is the change in angular velocity, and Δt is the change in time.

3. What is the unit of measurement for angular acceleration?

The unit of measurement for angular acceleration is radians per second squared (rad/s²) in the SI system. In other systems, it may also be measured in degrees per second squared (°/s²).

4. How does angular acceleration relate to linear acceleration?

Angular acceleration and linear acceleration are related because they both measure how quickly an object's motion is changing. However, angular acceleration measures changes in rotational motion, while linear acceleration measures changes in straight-line motion.

5. What factors affect the angular acceleration of an arm?

The angular acceleration of an arm can be affected by several factors, such as the force being applied to the arm, the mass and distribution of the arm's weight, and any external forces acting on the arm. Additionally, the length and shape of the arm can also affect its angular acceleration.

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