Lecture 24

Summary

Rotational energy
Torque
Newton's second law for rotation

Today's joke

Rolling motion

combine translation & rotation

Example #1

Rolling down an incline applet

Example #2

Rolling race down a ramp interactive
BU rolling down ramp applet
This applet graphs the total mechanical energy (purple), gravitational potential energy (red), translational kinetic energy (green), and rotational kinetic energy (blue) as various objects roll down a ramp. Notice that for the hoop, half its kinetic energy is translational and half is rotational, so the green and blue curves overlap, that's why you cannot see the green.

gc6 8.21
The tires of a car make 65 revolutions as the car reduces its speed uniformly from 95 km/h to 45 km/h. The tires have a radius of 0.40 m. What is the angular acceleration of the tires?
A. −0.661 rad/s²
B. −1.65 rad/s²
C. −4.13 rad/s²
D. −10.3 rad/s²
Answer

pse6 10.53
Determine a_CM of a uniform solid disk rolling down an incline making angle θ with the horizontal.
A. (g sin θ)/4
B. 2g/ sin θ
C. (g sin θ)/2
D. 2(g sin θ)/3
Answer

answer

C. −4.13 rad/s²
Picture (974x325, 9.7Kb)

answer

D. 2(g sin θ)/3
solution equation

Alternatively, you can use energy methods to find the speed of the disk at the bottom of the ramp, then use the initial and final speeds, and the distance traveled, to find the acceleration of the center of mass.

science saves lives joke