Finding resultant velocity from angular acceleration

In summary, the problem involves Michael spinning a rope at a rate of 2.00 rad/s^2 while running towards a target at 4.00m/s^2. The distance between his elbow and the end of the rope is 1.2m and he takes 3 seconds before launching the rope. To find the resultant velocity of the rope when it leaves his hand, we need to convert the angular acceleration to angular velocity and then relate it to the linear velocity using kinematic equations.
  • #1
Michael Fox
1
0

Homework Statement


Michael starts spinning the rope at a rate of 2.00 rad/s^2 while he starts running towards the target at 4.00m/s^2. This distance betweens Michael's elbow and the end of the rope form a straight 1.2m segment. If Michael takes 3 seconds before he launches the rope at the target, what is the resultant velocity of the rope when it leaves Michael's hand.

Homework Equations


at= (v2-v1)/2 (i think)
at=ra (at= linear acceleration, a = angular acceleration)

The Attempt at a Solution


I believe to solve I would have to convert angular acceleration to angular velocity but I cannot figure out how to do that. Any help clarifying or a diagram would be huge. Thank you for reading
 
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  • #2
What is the relation between angular acceleration and angular velocity? What is the relation between angular velocity and velocity?
 
  • #3
You probably have some kinematic equations that can handle that "transformation".
 

Related to Finding resultant velocity from angular acceleration

1. How do you calculate resultant velocity from angular acceleration?

To calculate resultant velocity from angular acceleration, you can use the formula v = ωr, where v is the resultant velocity, ω is the angular acceleration, and r is the radius of the circular motion.

2. 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 angular velocity is changing.

3. Can angular acceleration be negative?

Yes, angular acceleration can be negative. A negative angular acceleration means that the object is slowing down its rotation or changing its direction of rotation in a negative direction.

4. How is angular acceleration related to linear acceleration?

Angular acceleration and linear acceleration are related through the equation a = αr, where a is the linear acceleration, α is the angular acceleration, and r is the radius of the circular motion. This equation shows that the linear acceleration is directly proportional to the angular acceleration and the radius of the circular motion.

5. What is the unit of angular acceleration?

The unit of angular acceleration is radians per second squared (rad/s²). This unit represents the change in angular velocity (radians per second) over time (seconds).

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