Question

A meterstick is initially standing vertically on the floor. If the meterstick falls over, with what angular velocity will it hit the floor? Assume that the end in contact with the floor experiences no friction and slips freely.

Answer 1

The question inquires about the angular velocity of a falling meterstick, which relates to rotational motion and angular velocity in physics. However, without further details on mass distribution, an exact numerical answer cannot be determined.

Step-by-step explanation:

The question asks about the angular velocity with which a meterstick will hit the floor when it falls over from a vertical position, assuming the end in contact with the floor slips freely with no friction. To determine this, we would typically apply principles of conservation of energy and the dynamics of rigid body rotation. However, without information on the mass distribution of the meterstick or additional details, the exact angular velocity cannot be calculated. Although this question is related to physics concepts like rotational motion and angular velocity, it does not provide enough information to give a specific numerical answer.

Answer 2

L = length of the meter stick = 1 m

h = height of center of mass of stick from bottom end on the floor = L/2 = 1/2 = 0.5 m

m = mass of the meter stick

I = moment of inertia of the meter stick about the bottom end

w = angular velocity as it hits the floor

moment of inertia of the meter stick about the bottom end is given as

I = m L²/3

using conservation of energy

rotational kinetic energy of meter stick as it hits the floor = potential energy when it is vertical

(0.5) I w² = m g h

(0.5) (m L²/3) w² = m g h

( L²) w² = 6g h

( 1²) w² = 6 (9.8) (0.5)

w = 5.4 rad/s