Help please. Trigo, Angle measurement :(

[kinuel8091]

A pulley with a radius of 14 inches uses a belt to drive a pulley with a radius of 28 inches. The 14-inch pulley turns through an angle of 120°. Find the angle through which the 28-inch pulley turns.

Thanks!

 

[DrPhil]

A pulley with a radius of 14 inches uses a belt to drive a pulley with a radius of 28 inches. The 14-inch pulley turns through an angle of 120°. Find the angle through which the 28-inch pulley turns.

Thanks!

Since the belt doesn't shrink or stretch, rhe distance a point moves on the circumference of the smaller circle is equal to the distance on the larger circle. If you don't see right away how to use ratios, do the problem in two steps:
1) write a formula for the distance moved when the smaller wheel rotates 120°
2) use that distance to find the angle the larger wheel rotates.

Show us your work so we can see where you are stuck!

 

[kinuel8091]

Since the belt doesn't shrink or stretch, rhe distance a point moves on the circumference of the smaller circle is equal to the distance on the larger circle. If you don't see right away how to use ratios, do the problem in two steps:
1) write a formula for the distance moved when the smaller wheel rotates 120°
2) use that distance to find the angle the larger wheel rotates.

Show us your work so we can see where you are stuck!

S=rΘ
Where,
S= Arc covered by the angle
r= radius
Θ=Angle in radians


S=(14inches)x(120°x(π/180))
S=(14inches)x(2π/3)
S=28π/3

How can I use this?
Am i going to use the Radius of the larger pulley and the Arc Covered by this angle?

 

[DrPhil]

S=rΘ
Where,
S= Arc covered by the angle
r= radius
Θ=Angle in radians


S=(14inches)x(120°x(π/180))
S=(14inches)x(2π/3)
S=28π/3

How can I use this?
Am i going to use the Radius of the larger pulley and the Arc Covered by this angle?

YES.

Your variable S is measured in inches. On the larger pulley, S is the same number of inches, so the corresponding angle (in radians) will be

$\displaystyle \theta = S/r = \dfrac{28\ \pi/3}{28} = \cdot \cdot \cdot$

 

[kinuel8091]

YES.

Your variable S is measured in inches. On the larger pulley, S is the same number of inches, so the corresponding angle (in radians) will be

$\displaystyle \theta = S/r = \dfrac{28\ \pi/3}{28} = \cdot \cdot \cdot$

π/3
Thanks! it helped a lot!