Rotational motion, energy conservation problem

In summary, the problem involves a uniform rod of mass 2 kg and length 2m, pivoted from its end with a point mass of 1 kg on its tip. It starts at rest at an angle of 30 degrees above horizontal and falls under the influence of gravity. The question asks for the speed of the tip when the rod is horizontal at θ=0. Using the equation mgh=1/2mv^2, the solution is v=√2g=4.42. However, the given answer is 4.8. The problem also asks for the rotational kinetic energy of the system and the total change in gravitational potential energy as it falls.
  • #1
leapinlizards
1
0
rotational motion, energy conservation problem URGENT please help

Homework Statement



A uniform rod of mass M=2 kg and length L = 2m is pivoted from its end. It has a point mass m=1 kg on its tip. It stars from rest at an angle of 30 degrees above horizontal. It falls under the influence of gravity. How fast is the tip m moving when the rod is horizontal at θ
= 0

Homework Equations



mgh = 1/2mv^2

The Attempt at a Solution



h= Lsinθ = 1
m cancels from both sides
so you're left with
v=√2g=4.42

BUT, the actual answer given is 4.8

Help please! I have a test in just a few hours and have been trying to figure this problem out for awhile! Thanks
 
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  • #2


How would you write the rotational KE of the system? Also, what's the total change in gravitational PE as it falls?
 

FAQ: Rotational motion, energy conservation problem

What is rotational motion?

Rotational motion is the movement of an object around a fixed axis. This type of motion is commonly seen in objects such as wheels, gears, and planets.

How is rotational motion different from linear motion?

Rotational motion involves an object moving around an axis, while linear motion involves an object moving in a straight line. Additionally, rotational motion can involve changes in both the object's position and orientation, while linear motion only involves changes in position.

How is energy conserved in rotational motion?

Energy is conserved in rotational motion through the principle of conservation of angular momentum. This means that the total angular momentum of a system remains constant, even if individual objects within the system experience changes in their rotational motion.

What types of problems can be solved using energy conservation in rotational motion?

Energy conservation can be applied to problems involving objects rotating around a fixed axis or problems involving changes in an object's rotational motion over time. It can also be used to calculate the amount of energy required to change an object's angular velocity or to determine the final velocity of an object after rotating a certain distance.

How can I calculate the moment of inertia for an object in rotational motion?

The moment of inertia for an object in rotational motion can be calculated using the formula I = mr^2, where m is the mass of the object and r is the distance from the object's axis of rotation. This formula can be used for simple shapes such as spheres and cylinders, but more complex objects may require more advanced calculations.

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