Linear and Angular Speed???

Question

The circular blade on a saw has a diameter of 7.5 inches and rotates at 2400 revolutions per minute.

A.) Find the angular speed in radians per second.
B.) Find the linear speed in of the saw teeth (in feet per second) as they contact the wood being cut.

Answer 1

Question A
1 rev = 2π radians

2400 revs /min = 4800 π radians / min
= 80 π radians / sec
Angular speed ω = 251.3 radians / sec

Question B
v = ωr
v = 251.3 x 3.75 / 12 ft / sec
v = 78.5 ft /sec

Answer 2

the dis meter = 7.5 in

so radius = 7.5/2 = 3.75 in

rev per minute = 2400

so rev per second = 2400/60 = 40

A)

angular speed = 2 pi *(revolutions per second)

=>2pi(40) = 80 pi = 251.33 radians/sec

B)

linear speed = radius* (angular speed)

=>3.75(251.33) = 942.5 in/s = (942.5/12) = 78.5 ft/s

Answer 3

A) 2400 (rev/min) * 2pi (rads/rev) * 1/60 (min/sec) = 251.3 rads/sec

Misread, the first time: r = 7.5/2 = 3.75
B) 251.3 (rads/sec) * 3.75 in * 1/12 (ft/in) = 78.5 ft/sec