10-6 Rotational Dynamics; Torque and Rotational Inertia(Page: 280-282) N- I Law for rotation(定轴转动定律)(P244) A rotational rigid body can be considered to be constituted by many parts. The ith part has a mass Am external force Fi internal force f; Applying n- I law on△m2 JA F+f=△ Resolving it into directions t and n: :f+f=△m1ait=△m;ra
10-6 Rotational Dynamics; Torque and Rotational Inertia (Page:280-282) external force ; Fi i f internal force Applying N-II law on mi: Fi f i mi a + = z o i r i f Fi mi ˆ : Fi t + f i t = mi ai t = mi ri A rotational rigid body can be considered to be constituted by many parts. The ith part has a mass mi , Resolving it into directions and : ˆ n ˆ 1. N-II Law for Rotation (定轴转动定律) (P244)
&Sum:∑F+∑/=|∑△mh2la n F lni s fi 0and∑fr1=0 S0, we have∑Fn=∑△mtr2a met s Let tnet=∑ ∑Fn Net torque about given axis, and
+ = i i i i i t i i i t i F r f r m r 2 & sum: i r n ˆ : Finri = f inri = 0 = 0 i i i and f r So, we have = i i i i it i F r m r 2 = = i net i it i Let F r —— Net torque about given axis, and
I=△m;r; -the moment of inertia or rotational inertia(转动惯量) on the axis Then, Inet=Ia N-Il Law for Rotation(p244) Net torque on a rigid body equals to the product of rotational inertia and angular acceleration it causes about same axis
—— the moment of inertia or rotational inertia (转动惯量) on the axis. = 2 i i I m r Then, net = I N-II Law for Rotation(p244) —— Net torque on a rigid body equals to the product of rotational inertia and angular acceleration it causes about same axis
Comparing with the translation, this equation has the same importance like the Newton's second law for a single particle The moment of inertia is a measure of the rotational inertia of a body, which plays the same role for rotational motion that mass does for translational motion. (p245)
Comparing with the translation, this equation has the same importance like the Newton’s second law for a single particle. The moment of inertia I is a measure of the rotational inertia of a body, which plays the same role for rotational motion that mass does for translational motion.(p245)
中文推导 1)单个质点m与转 轴刚性连接 F=ma,=mra A. F M=resin e M=rf=mra M=mra 2)刚体 质量元受外力尸,内力 F M+M.=△mr2 外力矩 内力矩
O r m z F Ft Fn M = rFsin Ft = mat = mr 2 ej ij j j M + M = m r 2）刚体 质量元受外力 ，内力 Fej Fij M 1）单个质点 与转 轴刚性连接 m 外力矩 内力矩 2 M = mr 2 M = rFt = mr O z mj j r Fej Fij 中文推导