Determine the Magnitude of the Time Rate of Change of Angular Momentum

In summary, the conversation discusses an experiment involving an individual throwing a rock with an initial horizontal velocity of 20 ft/s from the edge of a cliff at a height of 50 ft. The task is to determine the magnitude of the time rate of change of the angular momentum of the rock at t=1s. The equations r = 50 ft j and HO = rXmv are mentioned, and there is a question about finding the force from the given velocity. The individual is seeking help in deriving equations for the horizontal and vertical speeds at time t.
  • #1
Northbysouth
249
2

Homework Statement


In an experiment an individual throws a rock with an initial horizontal velocity of v0 = 20 ft/s at time t=0. The rock is thrown from the edge of a cliff (directly above the base of the cliff) at height h=50 ft from the ground. The origin is assigned at the base of the cliff. Determine the magnitude of the time rate of change of the angular momentum of the rock about O (H'O) at time t = 1 second


Homework Equations



HO = rXmv

H'O = MO

The Attempt at a Solution



I think that r = 50 ft j

But how do I find the force from the given velocity?

Any help would be appreciated.
 
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  • #2
What force?
Can you write down equations for the horizontal and vertical speeds at time t?
 

FAQ: Determine the Magnitude of the Time Rate of Change of Angular Momentum

What is angular momentum?

Angular momentum is a measure of the rotational motion of an object. It is defined as the product of an object's moment of inertia and its angular velocity.

How is the time rate of change of angular momentum calculated?

The time rate of change of angular momentum, also known as angular acceleration, is calculated by dividing the change in angular momentum by the change in time. This can be expressed mathematically as dL/dt = (L2 - L1)/(t2 - t1), where dL is the change in angular momentum and dt is the change in time.

Why is it important to determine the magnitude of the time rate of change of angular momentum?

The magnitude of the time rate of change of angular momentum is important because it tells us how quickly an object's angular momentum is changing. This can help us understand the forces acting on the object and predict its future motion.

What are some real-world examples of angular momentum and its time rate of change?

Some examples of angular momentum and its time rate of change include the rotation of planets and celestial bodies, the spinning of a top, the motion of a spinning gyroscope, and the rotation of a bicycle wheel.

How does the time rate of change of angular momentum relate to conservation of angular momentum?

The time rate of change of angular momentum is related to conservation of angular momentum through the principle of angular momentum conservation. This principle states that the total angular momentum of a system remains constant unless acted upon by an external torque. Therefore, if there is no external torque acting on a system, the time rate of change of angular momentum will be zero, indicating that angular momentum is conserved.

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