Problem 9.3 Consider an object undergoing a rotational motion in the xy-plane about a fixed axis perpendicular to the plane of motion (Fig. 9.35). Let O be a point in the xy-plane along the axis of rotation and P is a fixed point on the object. Due to the rotation of the object, point P will experience a circular motion with the radius of its circular path r = 0.6 m. Assume that at some point in time, the angular acceleration of the point P is a = 5rad/s and an angle between the vectors of its tangential and net acceleration is ß = 30°. Determine the magnitudes of linear velocity (v) of point P and the magnitude of its tangential (at), normal (an), and net (a) acceleration vectors.

Problem 9.3 Consider an object undergoing a rotational motion in the xy-plane about a fixed axis perpendicular to the plane of motion (Fig. 9.35). Let O be a point in the xy-plane along the axis of rotation and P is a fixed point on the object. Due to the rotation of the object, point P will experience a circular motion with the radius of its circular path r = 0.6 m. Assume that at some point in time, the angular acceleration of the point P is a = 5rad/s and an angle between the vectors of its tangential and net acceleration is ß = 30°. Determine the magnitudes of linear velocity (v) of point P and the magnitude of its tangential (at), normal (an), and net (a) acceleration vectors.

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

Rigid Body

A rigid body is an object which does not change its shape or undergo any significant deformation due to an external force or movement. Mathematically speaking, the distance between any two points inside the body doesn't change in any situation.

Rigid Body Dynamics

Rigid bodies are defined as inelastic shapes with negligible deformation, giving them an unchanging center of mass. It is also generally assumed that the mass of a rigid body is uniformly distributed. This property of rigid bodies comes in handy when we deal with concepts like momentum, angular momentum, force and torque. The study of these properties – viz., force, torque, momentum, and angular momentum – of a rigid body, is collectively known as rigid body dynamics (RBD).

Question

h
at
a
P
An
Ay
Fig. 9.35 Problems 9.2 and 9.3

Problem 9.3 Consider an object undergoing a rotational motion
in the xy-plane about a fixed axis perpendicular to the plane of
motion (Fig. 9.35). Let O be a point in the xy-plane along the axis
of rotation and P is a fixed point on the object. Due to the
rotation of the object, point P will experience a circular motion
with the radius of its circular path r =
0.6 m.
Assume that at some point in time, the angular acceleration of
the point P is a = 5rad/s and an angle between the vectors of its
tangential and net acceleration is ß = 30°.
Determine the magnitudes of linear velocity (v) of point P and
the magnitude of its tangential (at), normal (an), and net (a)
acceleration vectors.
Answers:
1.02 m/s; at = 3 m/s²; an =1.72 m/s²; a = 3.46 m/s²
7) =

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