Angular Acceleration: Propellor on Boat Increases from 50 to 150 rev/min

In summary, the problem involves determining the angular acceleration of a propellor on a boat that experiences a constant acceleration from 50 rev/min to 150 rev/min in 2.5 seconds. The kinematic equations for rotational motion can be applied, similar to those used for translational motion, to solve for the acceleration. Thinking about the problem in terms of linear motion and finding a rotational equivalent may also help clarify the solution.
  • #1
petal5
26
0
The problem is:

The angular speed of a propellor on a boat increases with constant acceleration from 50 rev/min to 150rev/min in 2.5s.What is the angular acceleration of the propellor?

I'm not sure how to go about the problem.So far I've converted the 50rev/min and the 150rev/min to rad/s.Do I have to work out wf-wi and tf-ti or am I going about it wrong?
Thanks!
 
Last edited:
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  • #2
petal5 said:
Do I have to work out wf-wi and tf-ti or am I going about it wrong?
Sounds like you are on the right track.
 
  • #3
Kinematic equations can be applied to translational motion with constant acceleration. The same works in rotational dynamics. In fact, the equations for both types of motion share a common format with different variables. Given an initial and final angular speed during some time interval, what is the acceleration? If you're still unsure, ask yourself, "How would I solve if the variables were dimensionally linear?" Is there a similar rotational equivalent?
 

FAQ: Angular Acceleration: Propellor on Boat Increases from 50 to 150 rev/min

What is angular acceleration?

Angular acceleration is a measure of how quickly the angular velocity of an object changes over time. It is typically measured in units of radians per second squared (rad/s^2).

Why is the propellor on the boat increasing from 50 to 150 rev/min?

The propellor on the boat is increasing in speed in order to generate more thrust and propel the boat forward at a faster rate. This can be useful in situations where the boat needs to speed up or overcome resistance from currents or waves.

How is angular acceleration related to linear acceleration?

Angular acceleration is related to linear acceleration through the equation a = rα, where a is linear acceleration, r is the distance from the axis of rotation to the point of interest, and α is angular acceleration. In other words, as angular acceleration increases, linear acceleration will also increase if the distance from the axis of rotation remains constant.

Can angular acceleration be negative?

Yes, angular acceleration can be negative. This indicates that the angular velocity is decreasing over time, either due to a decrease in speed or a change in direction of rotation.

How does the propellor on the boat affect the boat's angular acceleration?

The propellor on the boat affects the boat's angular acceleration by changing the torque applied to the boat. As the propellor spins faster, it creates more torque, which results in a larger angular acceleration. This, in turn, increases the boat's overall speed and acceleration.

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