同济大学：《大学物理》课程教学资源（电子教案，英文版）第六章 刚体的转动（下）.

Motion of Rigid body (II)

Motion of Rigid body (II)

Agenda today 1.Work done in rotation 2.Rolling 3.Angular momentum 4.Conservation law of angular momentum 5.Procession

Agenda today 1.Work done in rotation 2. Rolling 3. Angular momentum 4. Conservation law of angular momentum 5. Procession

Work done in rotation w=正=m-a0 =J-0-gr20 power dw =T0 d

Work done in rotation power：       dt d dt dW P             2 1 2 1 2 1 2 1 2 1 2 2 2 1 2 1                   d J d d dt d J W E J J J d net

Torque due to gravity: 手 李茗 The torque of gravity exert on a certain rigid body is equivalent to the one on a same weighted particle placed at the mass center of the body

Torque due to gravity: The torque of gravity exert on a certain rigid body is equivalent to the one on a same weighted particle placed at the mass center of the body

Gravitational potential energy of a rigid body E,=∑△m,g,=m ∑△m,21=mg2e m The gravitational potential energy of a rigid body is as same as the energy of one particle on its center of mass with same weight The work-energy theorem of rotation e02 2 二J0

Gravitational potential energy of a rigid body c i i p i i mgz m m z E m gz m g      The gravitational potential energy of a rigid body is as same as the energy of one particle on its center of mass with same weight The work-energy theorem of rotation                  2 1 1 2 2 2 2 1 2 2 1 1       d mgz J mgz J ext c c

Trebachet

Trebachet

a M 80 m b 0

Counterweight mass is to be M 10,000kg (10 tons),and projectile mass is m 100 kg. The length of the main beam is that of the short lever arm plus long lever arm:L 1 12 m.The Mass of the beam is 2,000 kg. This is a realistic value for an oak mass of the main beam that is 12m long.0=45 degrees

• Counterweight mass is to be M 10,000kg (10 tons), and projectile mass is m 100 kg. The length of the main beam is that of the short lever arm plus long lever arm: L + l = 12 m. The Mass of the beam is 2,000 kg. This is a realistic value for an oak mass of the main beam that is 12m long. 0=45 degrees

Find the maximum range cover by the projectile a)If the mass of the beam is not considered b)If the mass of beam is considered

• Find the maximum range cover by the projectile a) If the mass of the beam is not considered b) If the mass of beam is considered