A ball with radius 12cm rolls on a level surface, and the translational speed of the center of mass is 0.35 m/s.
What is the angular speed about the center of mass if the ball rolls without slipping?
in a .12*2*PI path, it has rolled once.
time= distance/speed= 12*2*PI/.35 s
angulur apeed= 2PI/time
To find the angular speed about the center of mass when the ball rolls without slipping, we can use the formula:
Angular Speed (ω) = Translational Speed (v) / Radius (r)
In this case, the translational speed (v) is given as 0.35 m/s and the radius (r) of the ball is 12 cm. However, we need to convert the radius to meters before calculating the angular speed.
Converting the radius of the ball from cm to meters:
12 cm = 12/100 m = 0.12 m
Now, we can substitute the values into the formula:
Angular Speed (ω) = 0.35 m/s / 0.12 m
Calculating the angular speed:
ω = 0.35 / 0.12 ≈ 2.92 rad/s
Therefore, the angular speed about the center of mass when the ball rolls without slipping is approximately 2.92 rad/s.