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Rigidity (electromagnetism) - In accelerator physics, rigidity is a concept used to determine the effect of particular magnetic fields on the motion of the charged particles. It is a measure of the momentum of the particle, and it refers to the fact that a higher momentum particle will have a higher resistance to deflection..
Rigid body dynamics - In physics, rigid body dynamics is the study of the motion of rigid bodies. Unlike particles, which move only in three degrees of freedom ( translation in three directions), rigid bodies occupy space and have geometrical properties, such as a center of mass, moments of inertia, etc.,..
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Motion of Particles and Rigid Body
Introduction - Physicists love to look at something complicated and find in it, something simple and familiar. Here is an example. If you flip a baseball bat into the air, its motion as it turns, is clearly more complicated than that of a non-spinning tossed ball, which moves like a parti..
..Motion of Particles and Rigid Body Summary
Summary - The centre of mass is an imaginary point where one can assume the entire mass of the given system or object to be positioned. Principle of conservation of linear momentum states that the linear momentum of a system remains constant if the external forces acting on the system add up to zer..
Fluid Dynamics - Rigid Body motionA ball being thrown into a pool of fluid.
Leaving Cert Applied Maths Rigid Body MotionRigid Body Motion question 6(a), page 330 Homepage: www.thephysicsteacher.ie Blog: ozymandias1.wordpress.com
Question : http://www.geocities.com/super_cowling/diagram.JPG
5 isoceles right-angled triangular laminas, each uniform with mass m and base 2a are put together to form another lamina, shown in the diagram. MI of the combined lamina about an axis l through V, perpendicular to its plane is 58/3 ma^2. The axis l is horizonatal, and the combined lamina makes small oscillations under gravity about l. At time t the angle between VO and the vertical is . Write down the eqn of motion of the combined lamina an..
Answer : centre of mass of (upper triangle+square of side 2a) is - centre of mass of upper triangle = a/3 from the base. (pappu's therom or using integration method) Centre of mass of the system = [(4 m a) - (m a/3) ]/ 5 m = (11 a)/15 (from the mid-line of square and triangle) or centre of mass from v = 26 a /15 Restoring torque = (5 m g) [ (26 a /15) sin ] for small ' ' , sin is approximated to I = - (26/3) m g a where I = 58/3 ma^2 58/3 m a^2 = - (26/3) m g a = - (13/29) g/a comparing with = - ^2 ^2 = 13/29 g/a T = 2 / T = 2 (29a/13g)
Answer : centre of mass of (upper triangle+square of side 2a) is - centre of mass of upper triangle = a/3 from the base. (pappu's therom or using integration method) Centre of mass of the system = [(4 m a) - (m a/3) ]/ 5 m = (11 a)/15 (from the mid-line of square and triangle) or centre of mass from v = 26 a /15 Restoring torque = (5 m g) [ (26 a /15) sin ] for small ' ' , sin is approximated to I = - (26/3) m g a where I = 58/3 ma^2 58/3 m a^2 = - (26/3) m g a = - (13/29) g/a comparing with = - ^2 ^2 = 13/29 g/a T = 2 / T = 2 (29a/13g)
Question : If an oblong object is on a frictionless surface and a force is applied to it's edge will it only have rotational motion or will it's center of mass have translational energy as well?
Answer : Great question! The answer is that its center of mass WILL move. For example, if you apply Force 'F' for a short time 't', regardless of what part of the body you apply it to, the object's center of mass will change its velocity according to the impulse equation: Ft = m v ...which is a consequence of the conservation of (linear) momentum. It will also (independently) spin, on account of the conservation of ANGULAR momentum.
Answer : Great question! The answer is that its center of mass WILL move. For example, if you apply Force 'F' for a short time 't', regardless of what part of the body you apply it to, the object's center of mass will change its velocity according to the impulse equation: Ft = m v ...which is a consequence of the conservation of (linear) momentum. It will also (independently) spin, on account of the conservation of ANGULAR momentum.