Can something moving linearly without rotation have anguar momentum?

[nabeel17]

I was doing a question in Taylor book (example 3.3) where a sticky putty is thrown at a stationary wheel. To solve it we use conservation of angular momentum. What I am confused about is that the wheel is initially at rest and has no angular momentum initially. But when the putty is thrown at it the wheel starts spinning and gains angular momentum. Since angular momentum must be conserved (external torque is 0 so angular momentum conserved) there must be some inital angular momentum from the putty.

So my question is even though the putty is thrown in a straight line and has no spin or rotational motion, it still posses angular momentum?

 

[D H]

So my question is even though the putty is thrown in a straight line and has no spin or rotational motion, it still posses angular momentum?

Yes.

Even a point mass has angular momentum with respect to some reference frame. That essentially is how angular momentum is defined. The angular momentum of a system of particles is the sum of the angular momenta of the individual particles.

 

[nabeel17]

Yes.

Even a point mass has angular momentum with respect to some reference frame. That essentially is how angular momentum is defined. The angular momentum of a system of particles is the sum of the angular momenta of the individual particles.

Ok so with respect to some origin, a point mass will have angular momentum given by rxp where where r is the distance from the origin. Even if it appears to be going straight with no rotation correct? So angular momentum is always defined with respect to an origin

 

[D H]

Exactly.

 

[PJC01]

Yes, it is possible for something moving linearly without rotation to have angular momentum. This is because angular momentum is a measure of an object's rotational motion, not just its linear motion. In the example you provided, the putty has linear momentum as it is thrown in a straight line, but it also has angular momentum because it is interacting with a spinning wheel. This interaction causes the putty to gain angular momentum, even though it is not rotating itself. This is a result of the conservation of angular momentum, which states that the total angular momentum of a system remains constant unless acted upon by an external torque. In this case, the external torque is provided by the interaction between the putty and the wheel, causing the putty to gain angular momentum and the wheel to spin. So, while linear motion and angular momentum are related, they are not the same and an object can have both at the same time.