Physics Please Explain Help! The blade on a table saw spins at 3300 rpm . Its diameter is 25.0 cm.?

A. Relationship between linear velocity v and angular velocity w is v = r * w where r = radius and w is in radians per second. Since it's given in rotations (2pi radians) per minute (60 seconds), you'll have to convert the units of w.

B. Convert the above velocity from m/s to mph.

As the blade rotates one time, a tooth on the edge of the blade moves a distance that is equal the circumference of the blade. In one minute, the blade rotates 3300 time. To determine the time for one revolution, invert this number.

t = 1/3300 minutes

One minute is 60 seconds.

t = 60/3300

The time is approximately 0.018 second.

C = π * 0.25

This is approximately 0.785 meter. To determine the speed of a tooth in m/s, divide the circumference of the blade by the time.

Speed = 0.25 * π ÷ 60/3300

Speed = 0.25 * 3300/60 * π = 13.75 * π

This is approximately 43.2 m/s.

1 mph * 5280 ft/mi * 12 in/ft * 2.54 cm/in * 1 m/100 cm * 1 h/3600 s = 0.44704 m/s

To convert m/s to mph, divide by this number.

13.75 * π ÷ 0.44704

This is approximately 97 mph.

(3300/60)/2 = 27.5 rad/sec.

Radius = 0.25 metre.

V = (0.25 x 27.5) = 6.875m/sec.

(6.875 x 3.6) x 0.6213) = 15.38 mph.