# Calculate Angular Momentum of 2kg Object at Time t

• vu10758
In summary, the angular momentum of a 2kg object with a position vector r = -4t i + 3t^2 j (m) relative to the origin is -24t^2 k (kgm^2/s). The formula for angular momentum is L = r*p, where p is the object's momentum. By differentiating r, the velocity v can be found to be -4 i + 6t j. The angular momentum can then be calculated by taking the cross product of r and v and multiplying by 2, resulting in a function of time with t in the result.
vu10758
A 2kg object has a position vector r = -4t i + 3t^2 j (m). Find its angular momentum relative to the origin as a function of time.

The correct answer is -24t^2 k (kgm^2/s).

I know that L = r*p and p is mv

so I differentiate r to get v

v = -4 i + 6t j

do I just multiply 2 and the cross proudct of r and v? I don't know what to do because of the t in the equation for vector r.

vu10758 said:
A 2kg object has a position vector r = -4t i + 3t^2 j (m). Find its angular momentum relative to the origin as a function of time.

The correct answer is -24t^2 k (kgm^2/s).

I know that L = r*p and p is mv

so I differentiate r to get v

v = -4 i + 6t j

do I just multiply 2 and the cross proudct of r and v? I don't know what to do because of the t in the equation for vector r.
Just do it. The angular momentum is to be found as a function of time. t will be in the result

Yes, you are on the right track. To calculate the angular momentum, you need to first find the velocity vector, which you have correctly done by differentiating r with respect to time. Next, you need to multiply the velocity vector by the mass of the object, which in this case is 2kg. This will give you the momentum vector, p. Finally, you can calculate the angular momentum by taking the cross product of r and p. The t in the equation for vector r will be cancelled out when taking the cross product, so you can simply plug in the values for the velocity vector and the mass to get the final answer of -24t^2 k (kgm^2/s).

## What is angular momentum?

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

## How is angular momentum calculated?

Angular momentum is calculated by multiplying the mass of the object by its velocity and the distance from the axis of rotation.

## What is the moment of inertia?

The moment of inertia is a measure of an object's resistance to changes in its rotational motion. It is determined by the object's mass and the distribution of its mass around its axis of rotation.

## What are the units of angular momentum?

The units of angular momentum are kilogram meters squared per second (kg m^2/s).

## Can angular momentum change?

Yes, angular momentum can change if there is a net external torque acting on the object. Without any external torque, angular momentum is conserved and remains constant.

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