Class 39: Center of mass Course Evaluation: 1. Started yesterday Apr - - PowerPoint PPT Presentation

Class 39: Center of mass

Course Evaluation:

• 1. Started yesterday Apr 13th, ends Dec 29th (Wednesday).
• 2. Go to http://pa.as.uky.edu/
• 3. Click at “UNDERGRADUATES” in the top menu and then choose the

first item: Physics & Astronomy Course Evaluations

• 4. Follow instructions from there.
• 5. Make sure remember or write down any given key or password. You

need this to re-enter the system if you cannot finish the evaluation in

• ne time.

Example

x F= -kx x=0

A 0.1kg mass is attached to a spring of spring constant 160N/m and set to oscillate. At t=0 the position of the mass is +2cm and moving with a velocity of +0.6m/s. Calculate . A, and  and then predict its position, veolicty, and acceleration at t=0.02s.

Six degrees of freedom

(x,y,z) (x,y,z)

You need: (i) Three parameters (coordinates) to fix the position of a point in the rigid body. (ii) Three angles to fix the orientation of the object. Translational motion Rotational motion

Center of mass

x y z

total i i i i i i i i N 2 1 N N 2 2 1 1 CM total i i i i i i i i N 2 1 N N 2 2 1 1 CM total i i i i i i i i N 2 1 N N 2 2 1 1 CM

M z m m z m m m m z m z m z m z M y m m y m m m m y m y m y m y M x m m x m m m m x m x m x m x

        

                          

m1 m2 m3 m4 m5

Example

1m 1m 1m 1m 1m 1m

Calculate the position of the CM of the uniform sheet of metal shown in the figure.