Two Wheels of Radii r and R

[nycmathguy]

Set 6.1
David Cohen

I am interested in 41 (a - d) only.

 

[MathLover1]

given:
r = 6 cm, R = 10 cm
and the angular speed of the larger wheel is ω=100 rpm,

ω= θ/t
So, θ = 100• 2pi radians
θ = 200pi radians
t=1min

a.
ω=100 rev/min to rad/min
ω=(100 rev/min)*(2πrad/rev)
ω=200π (rad/min)

b. the linear speed of the larger wheel
v=Rω
v=10cm*200π (rad/min)
v=6283cm/min

c. the angular speed of the smaller wheel, let it be ω1

two wheels have same linear speed, v

rω1=Rω
ω1=Rω/r
ω1=10*100 rpm/6
ω1=5*100 rpm/3
ω1=(500/3)rpm


d. determine the angular speed of the smaller wheel in radians per minute

convert ω1 to radians per minute

ω1=(500/3)(rev/min)*(2πrad/rev)=1000π/3(rad/min) -> approximately ω1=1047.2(rad/min)

 

[nycmathguy]

given:
r = 6 cm, R = 10 cm
and the angular speed of the larger wheel is ω=100 rpm,

ω= θ/t
So, θ = 100• 2pi radians
θ = 200pi radians
t=1min

a.
ω=100 rev/min to rad/min
ω=(100 rev/min)*(2πrad/rev)
ω=200π (rad/min)

b. the linear speed of the larger wheel
v=Rω
v=10cm*200π (rad/min)
v=6283cm/min

c. the angular speed of the smaller wheel, let it be ω1

two wheels have same linear speed, v

rω1=Rω
ω1=Rω/r
ω1=10*100 rpm/6
ω1=5*100 rpm/3
ω1=(500/3)rpm


d. determine the angular speed of the smaller wheel in radians per minute

convert ω1 to radians per minute

ω1=(500/3)(rev/min)*(2πrad/rev)=1000π/3(rad/min) -> approximately ω1=1047.2(rad/min)

I totally gave up on this one after 30 minutes of effort.