Answered: To study torque experimentally, you…

Physics for Scientists and Engineers: Foundations and Connections

1st Edition

ISBN:9781133939146

Author:Katz, Debora M.

Publisher:Katz, Debora M.

Chapter14: Static Equilibrium, Elasticity, And Fracture

Section: Chapter Questions

Problem 17PQ

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To study torque experimentally, you apply a force to a beam. One end of the beam is attached to a pivot that allows the beam to rotate freely. The pivot is taken as the origin or your coordinate system. You apply a force of F = F_x i + F_y j + F_z k at a point r = r_x i + r_y j + r_z k on the beam.

Part a) Calculate the magnitude of the torque, in newton meters, when the components of the position and force vectors have the values rx = 3.71 m, ry = 0.075 m, rz = 0.085 m, Fx = 1.2 N, Fy = -7.6 N, Fz = 1.2 N.

Part b) If the moment of inertia of the beam with respect to the pivot is I = 72 kg˙m^2, calculate the magnitude of the angular acceleration of the beam about the pivot, in radians per second squared.

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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