Ok, in one turn, the small wheel drags the belt of 2*pi*0.4
That is (2*pi*0.4) / (2*pi*1.2)th of the large wheel (ratio of the circumferences).
Hence 1 turn on the small wheel = 0.4/1.2 = 1/3 turn on the large wheel.
So the angular velocity of the large wheel is 10*1/3 = 3.3333... rad/s
Now, if we take the questions :
a)
The linear velocity is v = r * w
So v = 0.4 * 10 = 4m/s
The belt does not slip, therefore the velocity of the point at the edge and the velocity of the belt are the same -> 4m/s
b )
Same here, the velocity of the belt is a constant (or the belt would break, if a part if moving faster than another part :p)
-> the linear velocity of a point on the outside of gear 2 is also 4m/s.
c)
It's actually a) in reverse : v = r * w <--> w = v / r
So, the angular velocity of gear 2 is w = 4 / 1.2 = 3.3333... m/s
This post was edited by Witzard on Aug 21 2015 03:23pm