One gear wheel turns another, the teeth being on the rims. The wheels have 50 cm and 70 cm radii, and the smaller wheel rotates at 30 revolutions/minute. Find the angular speed of the larger...

Question

wheel in radians per second. (Note: the wheels have the same liner speed.)

Answer 1

Given:

Na = 30 rpm (smaller wheel)

Ra = 50 cm

Rb = 70 cm

Find:

wb = ? (Angular speed of bigger wheel)

Solution:

Frequency = f = N/60 (to convert to rev/s)

Angular Speed = 2 * π * f = 2 * π * (N/60) rad/s

Angular speed of smaller wheel = ω_A = 2 * π * (30/60)=π rad/s

At the point where the wheels meet, there is a line speed velocity match

V = ω * r

ω_A * r_A = ω_B * r_B

ω_B = ω_A * (r_A /r_B) = π * (50/70)= 2.24 rad/s

Answer 2

The circumference of the larger wheel is 7/5 that of the smaller

In the time the same wheel makes 1 revolution the larger makes 5/7 of a revolution.

The smaller wheel makes 30 rpm or an angular of 60π^r pm.

The larger wheel makes (5/7)(60π^r pm), or 42.85714π^r pm