Answered: A square metal plate with mass M=6.00…

Physics for Scientists and Engineers: Foundations and Connections

1st Edition

ISBN:9781133939146

Author:Katz, Debora M.

Publisher:Katz, Debora M.

Chapter1: Getting Started

Section: Chapter Questions

Problem 19PQ

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Question

A square metal plate with mass M=6.00 [kg] and side length 3.00 [m] is pivoted about an axis through point O at its center and perpendicular to the plate. Three forces of magnitude F₁=36.0 [N], F₂=24.0 [N], and F₃=40.0 [N] act on the plate as shown.

A. What is the net torque on the square plate due to these forces? Is the direction in or out of the paper?

B. What is the angular acceleration of the plate? The moment of inertia for a plate of length a and width b rotating about its center is I_com =(1/12) M(a² + b²) Is the direction in or out of the paper?

C. If the plate is initially at rest, what is the angular velocity of the particle after 2.70 [s] Is the direction in or out of the paper?

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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