# Rotational motion problem

A boy of mass m runs on ice with velocity v and steps on the end of a plank of length l and mass M perpendicular to his path.
Describe quantitatively the motion of the sytem.Neglect friction
One point on the plank is at rest immediately after the collision.Where is it?

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#### Curious3141

Homework Helper
The OP has not shown any work, but if this is the question he was given (verbatim), it's a piss poor question.

If friction is neglected, then I'd ask the question-setter to explain to me exactly how the boy is able to "run". And how would he be able to remain planted on the plank after he steps on it ?

Where is the plank sited ? Is it just lying at rest on the ice ? Or is it balanced on a fulcrum off the ground, like a see-saw ?

Using the former interpretation, and completely neglecting friction between plank and ice, why is this even a rotational movement problem ? There would be NO point on the plank remaining at rest with respect to the ice. Assuming the boy somehow remains on the plank without friction (thereby imparting all his momentum to the plank-boy combination), the plank-boy would travel with a velocity equal to $v\frac{m}{M+m}$ in the same direction as the boy's initial running.

#### OlderDan

Homework Helper
Curious3141 said:
The OP has not shown any work, but if this is the question he was given (verbatim), it's a piss poor question.

If friction is neglected, then I'd ask the question-setter to explain to me exactly how the boy is able to "run". And how would he be able to remain planted on the plank after he steps on it ?

Where is the plank sited ? Is it just lying at rest on the ice ? Or is it balanced on a fulcrum off the ground, like a see-saw ?

Using the former interpretation, and completely neglecting friction between plank and ice, why is this even a rotational movement problem ? There would be NO point on the plank remaining at rest with respect to the ice. Assuming the boy somehow remains on the plank without friction (thereby imparting all his momentum to the plank-boy combination), the plank-boy would travel with a velocity equal to $v\frac{m}{M+m}$ in the same direction as the boy's initial running.
If we give them a bit of a break on the problem statement, we could assume the boy started running before he got to the ice and just managed to keep his balance long enough the jump onto the plank, Then if we assume that "neglect friction" only applies to the plank and ice (not the plank and the boy) we potentially have a rotation problem. What we still need to know is where the boy jumps on the plank. If he jumps on the middle, you have solved the problem. If he jumps on off-center, the plank is going to rotate as well as slide, and one point initially at rest is a distinct possibility.

#### Doc Al

Mentor
The problem statement could be improved. I assume by "neglect friction" that they mean to neglect the friction between plank and ice, not between boy and ice (though he could be sliding at speed v) or certainly between boy and plank.
Using the former interpretation, and completely neglecting friction between plank and ice, why is this even a rotational movement problem ? There would be NO point on the plank remaining at rest with respect to the ice. Assuming the boy somehow remains on the plank without friction (thereby imparting all his momentum to the plank-boy combination), the plank-boy would travel with a velocity equal to $v\frac{m}{M+m}$ in the same direction as the boy's initial running.
That's the translational speed of the center of mass of the plank-boy. But the plank-boy will also rotate. So the question does make sense.

Edit: Dan beat me again!

#### Curious3141

Homework Helper
Yes, I misread the question, there will be rotation.

OlderDan said:
If he jumps on the middle, you have solved the problem. If he jumps on off-center, the plank is going to rotate as well as slide, and one point initially at rest is a distinct possibility.
The boy jumps onn the plank at the end with contact with the ice and perpendicular to the surface.

Curious3141 said:
If friction is neglected, then I'd ask the question-setter to explain to me exactly how the boy is able to "run". And how would he be able to remain planted on the plank after he steps on it ?
im really sorry i forgot to mention about the friction being neglected only between the plank and the ice but i do think that was OBVIOUS.Anyway you did figure that out later.

#### OlderDan

Homework Helper
The boy jumps onn the plank at the end with contact with the ice and perpendicular to the surface.
So, the problem involves conservation of linear momentum and angular momentum. Have you solved it? If not, figure out where the center of mass (CM) of the plank and boy will be, and think about how the CM will move, with rotation about the CM.

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