大一物理题.A uniform steel rod of length 1.20 m and mass of 6.40 kg has attached to each end a small ball of mass1.06 kg.The rod is constrained to rotate in a horizontal plane about a vertical axis through its midpoint.At a certain instant it is observed to be rotating with an angular speed of 39.0 rev/s.Because of axlefriction it comes to rest 32.0 s later.Assume a constant frictional torque.(a) Find the angular acceleration.(b) Calculate the retarding to
大一物理题.
A uniform steel rod of length 1.20 m and mass of 6.40 kg has attached to each end a small ball of mass
1.06 kg.The rod is constrained to rotate in a horizontal plane about a vertical axis through its midpoint.
At a certain instant it is observed to be rotating with an angular speed of 39.0 rev/s.Because of axle
friction it comes to rest 32.0 s later.Assume a constant frictional torque.
(a) Find the angular acceleration.
(b) Calculate the retarding torque exerted by axle friction.
(c) Determine the total work done by the axle friction.
(d) Calculate the number of revolutions executed during the 32.0 s.
(e) Now suppose that the frictional torque is known not to be constant.which,if any ,of the quantities abcd or d can still be computed without requiring any additional information?if any exists give its value
一把钢标尺长度1.20 重6.40公斤。每个末端有一个小球
1.06公斤。 钢尺在一个平面转动于一个垂直于它的轴且通过中心。
在某一瞬时以39.0 rev/s.的有角速度。 由于
摩擦，于32.0 s后停止。 假设有恒定的摩擦系数。
(a)求角加速度。
(b)计算轨摩擦施加的减速的扭矩。
(c)确定轨摩擦所做的功。
(d)计算在32.0期间钢尺转多少圈。
(e)如果摩擦力知道但不是恒定的。 再计算上述abcd。
第一个
设杆的转动惯量为I1 球的为I2
杆的转动惯量为I1=m1L^2/12 球的为 m2(L/2)^2*2=m2L^2/2
因为(I1+I2)α=T
T=F*L/2*2=FL
可以解出α
第二个
冲量矩等于角动量
因此(I1+I2)ω=FLt
第三个
W=(I1+I2)ω^2/2
第四个
W=FS 解出S
revolution=S/2πr
第五个
需要知道摩擦力和时间的函数关系.