A uniform rod of mass M and length L is held vertically by two strings of negligible mass, as shown below. The string on the right is cut and the bar falls, rotating about the left end. L/2 Mg Answer the following using the rotational form of Newton's second law for extended objects (1) 7 = la. (a) Immediately after the string is cut, what is the angular acceleration of the stick. (b) Is the angular acceleration constant during the fall? If not, is it decreasing or increasing as the bar falls?

A uniform rod of mass M and length L is held vertically by two strings of negligible mass, as shown below. The string on the right is cut and the bar falls, rotating about the left end. L/2 Mg Answer the following using the rotational form of Newton's second law for extended objects (1) 7 = la. (a) Immediately after the string is cut, what is the angular acceleration of the stick. (b) Is the angular acceleration constant during the fall? If not, is it decreasing or increasing as the bar falls?

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Concept explainers

Angular speed, acceleration and displacement

Angular acceleration is defined as the rate of change in angular velocity with respect to time. It has both magnitude and direction. So, it is a vector quantity.

Angular Position

Before diving into angular position, one should understand the basics of position and its importance along with usage in day-to-day life. When one talks of position, it’s always relative with respect to some other object. For example, position of earth with respect to sun, position of school with respect to house, etc. Angular position is the rotational analogue of linear position.

Question

A uniform rod of mass M and length L is held vertically by two strings of negligible
mass, as shown below. The string on the right is cut and the bar falls, rotating about
the left end.
L/2
Mg
Answer the following using the rotational form of Newton's second law for extended
objects
(1)
7 = la.
(a) Immediately after the string is cut, what is the angular acceleration of the stick.
(b) Is the angular acceleration constant during the fall? If not, is it decreasing or
increasing as the bar falls?
The moment of inertia of a rod of length L and mass M rotating about an axis at the
end is given by I = {ML².
Note: The net gravitation force (and external force) acting on an extended object, is
equivalent to the force acting on a point mass M located at the center of mass. As a
result, the torque on the bar is determined by the force of gravity acting at the center
of mass.

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