# Angular momentum of ball spinning on a pendulum around a support point

• Los Frijoles
In summary, The problem is asking for the magnitude of the angular momentum of a ball spinning in a circle around a support point, with a given mass and rope length, making an angle of 37 degrees from the vertical. The angular momentum is dependent on the axis or point of calculation and can be calculated with the formula L = r x p, where r is the position vector and p is the relative velocity. In this case, the relative velocity is tangential to the circle and the position vector is perpendicular to it. This can be found by taking components of the position vector and using the vector cross product formula.
Los Frijoles

## Homework Statement

A ball (mass M: 0.250kg) is attached to a rope (length l: 1.69m) that is fixed to a point somewhere. The ball is spinning in a circle around the support point so that the rope makes an angle 37 degrees from the vertical. I have to find the magnitude of the angular momentum of the ball about the support point, which I can't figure out for the life of me.

## Homework Equations

r = sin37l = 1.02m
F = Mg = 0.250kg * 9.8m/s^2
t (torque) = r x F = rFsin90 = 1.02m(.250)(9.8) = 2.49 Nm
..as for getting the angular momentum all I know is:
L = r x p = mvr (in this situation)

## The Attempt at a Solution

Part of the question was to get the torque, which after getting it wrong once and being shown the answer (and then given different data...that's how the computer grading this works) I figured out that where I was previously doing t = rFsin37 that it needed to be rFsin90 since it is from the perspective of the anchor point. After trying to reverse engineer the answer I got back for the angular momentum I have come up with nothing and I have no idea how to figure it out.

I think the problem lies in that I need to somehow transform torque into the tangential velocity v required for the equation for L and I can't find anywhere in my textbook where it says that and I can't seem to find any relating equations except t = dL/dt (and I don't have any dt (and I haven't yet completed my calculus course...yay :/...))

Can anyone help me figure this out?

Hey,

This is a classic problem.

First thing you need to realize is that angular momentum and Torque are dependent on the axis (or point of calculation).

If you calculate the torque (or angular momentum) with respect to the centre of the circle and torque (or angular momentum)with respect to point of suspension you will get two different answers.

Net Torque of a particle about a point is given by R X F ,
where F is the net force acting on the particle ,(same with respect to all points as value of net force vector is frame independent ), and r is the position vector of the particle wrt that point.

The net force acting on the particle is it's mass times centripetal acceleration.
What is it?

What is its direction.?

What is the direction of R for the body?

(NOTE:you are wrong in considering net force as mg.Its something else and obviously dependent on 37 degrees).

the angular momentum about a point for a particle is defined again as m(R X v).

Remember R here is position vector of particle wrt that point, and v is its relative velocity wrt that point.

Now imagine the figure,

The relative velocity of the particle wrt point of suspension is tangential to the circle.

(WHY?)

What you need to realize now is that The vector R (which is along the string) is actually perpendicular to this velocity.

It is very important to realize that R is perpendicular to V.

One way to do it is to take components of R .

Take one component along the line joining the point of suspension and centre of the circle.
The other will now be along the line joining the particle and the centre of circle.

Both these components are perpendicular to the velocity, so R is perpendicular to velocity.

Use Formula to find magnitude.

A better way is to write everything in the form of vectors.

Take the line joining the centre of circle and suspension as one axis.

Take the other two axis along the radius of circle and tangential to it. These two axis move along with particle.

Write R, V and F in terms of vector and apply vector cross product. The advantage of this that it also gives you direction of the quantities in terms of vectors.

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## What is angular momentum?

Angular momentum is a measure of the rotational motion of an object around a fixed point or axis. It is calculated by multiplying the moment of inertia (a measure of the object's resistance to change in rotation) by the angular velocity (a measure of how quickly the object is rotating).

## How is angular momentum related to a ball spinning on a pendulum?

In the case of a ball spinning on a pendulum around a support point, the angular momentum is directly related to the ball's rotational motion around the support point. As the ball swings back and forth, its angular momentum will change due to the changing direction and speed of its rotation.

## What factors affect the angular momentum of a ball spinning on a pendulum?

The angular momentum of a ball spinning on a pendulum is affected by several factors, including the mass and velocity of the ball, the length of the pendulum, and the location of the support point. These factors can all impact the moment of inertia and angular velocity of the ball, thus affecting its angular momentum.

## How is angular momentum conserved in a system with a spinning ball on a pendulum?

According to the law of conservation of angular momentum, the total angular momentum of a system remains constant unless acted upon by an external torque. In the case of a spinning ball on a pendulum, the angular momentum of the ball is conserved as it swings back and forth, as long as there is no external torque present.

## What applications does understanding angular momentum of a ball spinning on a pendulum have?

Understanding the angular momentum of a ball spinning on a pendulum has various applications, including in physics and engineering. It can be used to analyze and design structures that involve rotational motion, such as bridges and amusement park rides. It also has implications in sports, particularly in understanding the mechanics of throwing and hitting objects.

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