Answered: The angular position of a rod varies as…

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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Question

The angular position of a rod varies as 23.7t² radians from time

t = 0. The rod has two beads on it as shown in the following figure, one at

r₁ = 15 cm from the rotation axis and the other at r₂ = 42 cm from the rotation axis. (Note: figure may not be drawn to scale.)

(a) What is the instantaneous angular velocity (in rad/s) of the rod at

t = 7 s?

(Indicate the direction with the sign of your answer. Round your answer to at least one decimal place.)

rad/s

(b) What is the angular acceleration (in rad/s²) of the rod at

t = 7 s?

(Indicate the direction with the sign of your answer.)

rad/s²

t = 7 s?

v_{t, 1}

= m/s

v_{t, 2}

= m/s

(d) What are the tangential accelerations of the beads at

t = 7 s?

(Enter the magnitudes in m/s².)

a_{t, 1}

= m/s²

a_{t, 2}

= m/s²

(e) What are the centripetal accelerations of the beads at

t = 7 s?

(Enter the magnitudes in m/s².)

a_{c, 1}

= m/s²

a_{c, 2}

= m/s²

Definition Definition Rate of change of angular velocity. Angular acceleration indicates how fast the angular velocity changes over time. It is a vector quantity and has both magnitude and direction. Magnitude is represented by the length of the vector and direction is represented by the right-hand thumb rule. An angular acceleration vector will be always perpendicular to the plane of rotation. Angular acceleration is generally denoted by the Greek letter α and its SI unit is rad/s 2 .

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