Angular Momentum of Clay + Device System: Calculations & Solution

[magma_saber]

Homework Statement

A device with 8 balls each with a mass of 0.8 kg is attached to spokes with length of 1.4 m, radius of 0.7 m. A lump of clay of 0.2 kg falls on the at the location shown and is attached to a ball at 45 degree angle. Before the impact, the clay was at a speed of 5 m/s. It moves counterclockwise with a angular speed of 0.08 radians/s.

What is the angular momentum of the system of the clay and devise?

Homework Equations

L_device = 1/2*M*R²
L_clay = r*p
L_system = L_device + L_system

The Attempt at a Solution

For the device, is the mass 8*0.08?
Also for the clay, is r just the radius?
Is this the right way to do this?

 

[LowlyPion]

A device with 8 balls each with a mass of 0.8 kg is attached to spokes with length of 1.4 m, radius of 0.7 m. A lump of clay of 0.2 kg falls on the at the location shown and is attached to a ball at 45 degree angle. Before the impact, the clay was at a speed of 5 m/s. It moves counterclockwise with a angular speed of 0.08 radians/s.

What is the angular momentum of the system of the clay and devise?

Homework Equations

L_device = 1/2*M*R²
L_clay = r*p
L_system = L_device + L_system

The Attempt at a Solution

For the device, is the mass 8*0.08?
Also for the clay, is r just the radius?
Is this the right way to do this?

First of all there is no diagram and so whichever of the spokes it lands on is not given. But said you angular momentum of the system is made of two parts.

L of spokes/blocks = I * ω

L of clay = r X P

But the r here is not the R of the spokes. It will be R*√2/2 which is the distance from the center along the axis that is ⊥ to the downward direction of P

Your I for the masses is apparently 8*.8*m*1.4²

 

[nlightner]

I would first clarify the units used in the problem. Are the masses given in kilograms or grams? Are the lengths given in meters or centimeters? This is important to ensure accurate calculations.

Next, I would begin by calculating the angular momentum of the device. The formula for angular momentum is L = I*ω, where I is the moment of inertia and ω is the angular velocity. In this case, the moment of inertia can be calculated using the formula I = 1/2*m*r^2, where m is the mass of the ball and r is the radius of the spoke. Plugging in the given values, we get I = 1/2*0.8*0.7^2 = 0.196 kg*m^2. Then, we can calculate the angular momentum of the device using Ldevice = I*ω = 0.196*0.08 = 0.01568 kg*m^2/s.

For the clay, the angular momentum can be calculated using the formula L = r*p, where r is the radius and p is the linear momentum. In this case, the radius is given as 0.7 m and the linear momentum can be calculated using p = m*v, where m is the mass of the clay (0.2 kg) and v is the velocity before impact (5 m/s). Plugging in the values, we get p = 0.2*5 = 1 kg*m/s. Therefore, the angular momentum of the clay is Lclay = r*p = 0.7*1 = 0.7 kg*m^2/s.

Finally, to calculate the angular momentum of the system, we can simply add the angular momenta of the device and the clay together. Lsystem = Ldevice + Lclay = 0.01568 + 0.7 = 0.71568 kg*m^2/s.

In summary, the angular momentum of the system of the clay and device is 0.71568 kg*m^2/s.