Atypical pencil has an average length of 15.0 cm and an average mass of 10.0 g. assume the tip of the pencil does not slip as it falls.
1. what is the angular acceleration of the pencil when it makes an angle of 10.0 degrees with the vertical? express your answer numerically in radians per second squared to three significant figures.

α = 17.0 rad/s²

Explanation:

For this problem let's use the torque expression

         τ = I α

Torque is the product of force by the distance that is half the length of the pencil

        τ = F x

Let's use trigonometry

        sin 10 = x / (l / 2)

        x = l / 2 sin 10

        τ = mg l /2  sin 10

The moment of inertia of pencil that we approximate as a rod with the axis of rotation at one end

          I = 1/3 m L²

 We replace

          mg l / 2 sin 10 = 1/3 m l² α

           α = 3/2 g/l  sin 10  

Let's reduce the magnitudes to the SI system

            l = 15.0 cm = 0.150 m

           m = 10.0 g = 0.0100 kg

Let's calculate

            α = 3/2 9.8 / 0.150 sin 10

            α = 17.0 rad/s²

relativism, roughly put, is the view that truth and falsity, right and wrong, standards of reasoning, and procedures of justification are products of differing conventions and frameworks of assessment and that their authority is confined to the context giving rise to them. more precisely, “relativism” covers views which maintain that—at a high level of abstraction—at least some class of things have the properties they have (e.g., beautiful, morally good, epistemically justified) not simpliciter, but only relative to a given framework of assessment (e.g., local cultural norms, individual standards), and correspondingly, that the truth of claims attributing these properties holds only once the relevant framework of assessment is specified or supplied. relativists characteristically insist, furthermore, that if something is only relatively so, then there can be no framework-independent vantage point from which the matter of whether the thing in question is so can be established.

relativism has been, in its various guises, both one of the most popular and most reviled philosophical doctrines of our time. defenders see it as a harbinger of tolerance and the only ethical and epistemic stance worthy of the open-minded and tolerant. detractors dismiss it for its alleged incoherence and uncritical intellectual permissiveness. debates about relativism permeate the whole spectrum of philosophical sub-disciplines. from ethics to epistemology, science to religion, political theory to ontology, theories of meaning and even logic, philosophy has felt the need to respond to this heady and seemingly subversive idea. discussions of relativism often also invoke considerations relevant to the very nature and methodology of philosophy and to the division between the so-called “analytic and continental” camps in philosophy. and yet, despite a long history of debate going back to plato and an increasingly large body of writing, it is still difficult to come to an agreed definition of what, at its core, relativism is, and what philosophical import it has. this entry attempts to provide a broad account of the many ways in which “relativism” has been defined, explained, defended and criticized.

explanation:

the word that best describes martin luther king jr.'s tone in the video is dignified

martin luther king, jr. was a social activist and baptist minister who played a key role in the american civil rights movement from the mid-1950s until his assassination in 1968. the video shows his manner and attitude having or showing a composed or serious manner that is worthy of respect so dignified is the correct answer