Translational and rotational motion

In summary, the question is asking for the mass M that would result in the stick having only translational motion after an elastic collision with it. This can be found by considering the conservation of momentum and the conservation of energy equations. The mass M needs to be in between a very light mass and a very heavy mass in order for the stick to have no rotational motion after the collision.
  • #1
Tonyt88
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1. A uniform stick of mass m and length l spins arounds on a frictionless horizontal table, with its CM stationary (but not fixed by a pivot). A mass M is placed on the plane, and the end of the stick collides elastically with it, as shown. What should M be so that after the collision the stick has translational motion, but no rotational motion?




2. This is where I get stuck



3. I'm hindered not only because I don't know which equations to apply, but also, I don't know what would result in the stick having just translational motion.
 
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  • #2
3. I'm hindered not only because I don't know which equations to apply, but also, I don't know what would result in the stick having just translational motion.[/QUOTE]

What equations do you usually use for problems involving impact? Hint: conservation of ...

If the mass was very light (like a speck of dust) the stick would just knock it out of the way and carry on rotating. If the mass was very heavy, the mass wouldn't move much, but the stick would bounce off and probably it would be rotating the opposite way. Somewhere in between, there is a mass where the rotation after the collision is zero. That's what you need to find.
 

Related to Translational and rotational motion

1. What is the difference between translational and rotational motion?

Translational motion is the movement of an object in a straight line, while rotational motion is the movement of an object around an axis or a fixed point. In translational motion, the object's entire mass moves together, while in rotational motion, different parts of the object have different speeds and directions of motion.

2. How do you calculate translational and rotational motion?

Translational motion can be calculated using the equation v=d/t, where v is velocity, d is distance, and t is time. Rotational motion can be calculated using the equation ω=θ/t, where ω is angular velocity, θ is angular displacement, and t is time.

3. What are some examples of translational and rotational motion in everyday life?

Examples of translational motion include walking, running, and driving a car in a straight line. Examples of rotational motion include the rotation of the Earth around its axis, the spinning of a top, and the movement of a fan blade.

4. How is translational and rotational motion related to Newton's Laws of Motion?

Newton's First Law, also known as the law of inertia, applies to both translational and rotational motion. An object in motion will continue to move in a straight line or at a constant rotation unless acted upon by an external force. Newton's Second Law, which states that force equals mass times acceleration, applies to translational motion. Newton's Third Law, which states that for every action there is an equal and opposite reaction, applies to both translational and rotational motion.

5. How does friction affect translational and rotational motion?

Friction can affect both translational and rotational motion by slowing down or stopping the motion of an object. In translational motion, friction between the object and the surface it is moving on can cause it to slow down or stop. In rotational motion, friction between the object and the axis it is rotating around can cause it to slow down or stop. Additionally, friction can also cause an object to rotate in a different direction than intended.

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