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Static Equilibrium and Elasticity

الكلية كلية التربية للعلوم الصرفة     القسم قسم الفيزياء     المرحلة 1
أستاذ المادة فؤاد عطية مجيد       29/05/2018 09:25:09
Rigid Body Kinematic
8.1 Rigid body
Object in the real world are not point- like particles that we have been dealing with up to now. A real object has a mass distribution associated whit its size and shape. The motion of the real object involves both:
Translational motion of the center of mass.
Rotational motion about an axis (usually take to be an axis through the center of mass or some other fixed axis). We will restrict our discussions to that of the rigid bodies. A rigid body is one in which the relative coordinates connecting all the constituent particles remain constant.
8.2 Rotation about a Fixed Axis
Consider motion around the z-axis. Reference point p represent the rotational motion of the body and of its angular position. Given a reference point p, its angular position is measured by the angle ?, between the position vector r ? and the x-axis. As the particle moves from the positive x- axis ?=0 to the point p it move through an arc length
S=r?, ?(rad)=?/180 ?(degree)
The rotational motion of a body is described by the rate of the change of ?. In general the position angle is a function of time [?=?(t)]. Suppose the particle moves from P to Q. the reference OP makes an angle ?_1 at the time t_1, and an angle ?_2 at the time t_2 . Define the average angular velocity of the body ? ? , in the time internal ?t=t_2-t_1 as the ratio of angular displacement
??=?_2-?_1 to ?t
? ?=(?-?_1)/(t_2-t_1 )=??/?t (rad/s)or (s)^(-1)
Analogous to linear velocity, the instantaneous angular velocity is defined as
? ?=lim?(?t?0)????/?t?=d?/dt (s)^(-1)
If the angular velocity, ? is a constant ?=?_0 the rate of rotation is often given in terms of the frequency, or number of revolution per unit time
1 revolution =??=2? radians
Time per revolution or period T=2?/?_0 (s)
Frequency of revolution is ?=1/T=?_0/2? (Hz)


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