Basic Motion of the Rigid Body

Abstract

In this chapter, we will learn two basic motions for the rigid body. The first one is translation and the second one is the rotation.

Exercises

• 8.1 As shown in Fig. 8.6, a circular disk is rotating with respect to the axis O. Its weight is W and its radius is R. At one certain time, the angular velocity of the disk is $\omega$ and angular acceleration is $\varepsilon$. Please give the expressions of the velocity and acceleration on the center of the disk.

  Fig. 8.6

  

  A disk in rotation with respect to one axis

• 8.2 What is the difference between one particle and one rigid body in translation? Please give the figure comparison.

• 8.3 As shown in Fig. 8.7, there are three bars moving. The bar AB is parallel to CD at any time, whose rotation velocity is n = 300 r/min. The length of the bar AB = CD = 150 mm. Please give the velocity and acceleration of the middle point of BC, i.e., point E.

  Fig. 8.7

  

  A mechanical system

Answers

• 8.1 $v_{c} = \omega R$, $a_{c}^{n} = \omega^{2} R$, $a_{c}^{\tau } = \varepsilon R$.

• 8.3 $v_{E} = 1.5\uppi\,{\text{m}}/{\text{s}}$, $a_{E}^{n} = 0\,{\text{m}}/{\text{s}}^{2}$, $a_{E}^{\tau } = 15\uppi\,{\text{m}}/{\text{s}}^{2}$.