What is the relationship between the angular velocities of two connected gears?

[cshelmo]

Homework Statement

a gear of radius 0.4m and a gear of radius 1.2m are connected by a belt. if the smaller gear is rotating with an angular velocity of 10 rad/s,
find the angular velocity of the larger gear.

here is the formula: v = rw

a. what can be said about the linear velocity of a point on the edge of gear 1 and the velocity of the belt?

b. because it is the movement of the belt that causes gear 2 to turn, what can be said about the linear velocity of a point on the outside of gear 2?

c. using the linear velocity of the points on the outside of gear 2, found in step b, and the radius of gear 2, find the gear's angular velocity.

d. what is the relationship between the angular velocity of gear1 and the angular velocity of gear 2?

Homework Equations

V= RW

The Attempt at a Solution

I cannot discover other gear radius or advance through the problem statement, apoligies for my lack of knowledge on this one..

 

[Dick]

a) and b) are not formula questions. They are 'use your head' questions. All points on the belt are moving at the same speed. What about points on the gears? How does their speed relate to the speed of the belt?

 

[o2bhoss]

A.) they would be equal
B.) The linear velocity on the outside of gear 2 should be equal to 4ms. (I think)
C.) v=rw so 4=1.2w so 2/1.2=w so w=3.333
D.) 1/3 the speed
E.) 1. the angular velocity will be greater in gear 2.
2. the angular velocity will be small in gear 2.
3. the angular velocity will be equal.

Plaese fell free to have these answers reviewed/checked. I think we are taking the same problem solving class.