A meter stick is held vertically with one end on the floor and is then allowed to fall. Find the speed of the other end when it hits the floor, assuming that the end on the floor does not slip. (Hint: Consider the stick to be a thin rod and use the conservation of energy principle.)

your initial PE turns to final PE and final rotational KE, right?

initial PE= mg(h/2)
final PE= mg(0)
rotational KE= 1/2 I w^2=1/2 I v^2/r^2

To find the speed of the other end of the meter stick when it hits the floor, we can use the conservation of energy principle.

Let's consider the system when the meter stick is held vertically with one end on the floor and the other end is released. At the beginning, the meter stick has gravitational potential energy equal to its initial height, and no kinetic energy. As the meter stick falls, it loses potential energy and gains an equal amount of kinetic energy.

According to the principle of conservation of energy, the total energy of a closed system remains constant. In this case, we assume that there are no external forces acting on the meter stick, and therefore, the total mechanical energy is conserved.

The gravitational potential energy of the meter stick at the starting position is given by the formula:

PE = m * g * h

Where m is the mass of the meter stick, g is the acceleration due to gravity (approximately 9.8 m/s^2), and h is the initial height of the meter stick.

When the meter stick is released and falls freely, all its potential energy is converted into kinetic energy. The kinetic energy of the meter stick just before hitting the floor is given by the formula:

KE = (1/2) * m * v^2

Where v is the speed of the other end of the meter stick just before it hits the floor.

Since the total mechanical energy is conserved, we can equate the initial potential energy to the final kinetic energy:

m * g * h = (1/2) * m * v^2

We can now solve this equation to find the speed of the other end of the meter stick when it hits the floor.

Dividing both sides of the equation by m, we get:

g * h = (1/2) * v^2

Multiplying both sides by 2, we get:

2 * g * h = v^2

Taking the square root of both sides, we finally get:

v = √(2 * g * h)

By substituting the values of g (9.8 m/s^2) and h (height of the meter stick) into the formula, we can easily calculate the speed v.