Question

Q) A physics instructor is in a dryer traveling at ω = 800 rad/s. Radius = 2 m Mass = 92 kg
a) How many revolutions per minute is he making?
b) What is the centripetal force on the instructor?
c) If he stops at Δt = 27 seconds, how many degrees has he traveled?

Answer 1

(a) w = 800 rad/s = (800*60) rad/min

now, 1 revolution = 2*pi radian

so, w = (800*60) / (2*pi) rev/min = 7641 revolutions/min.

(b) v = r*w

Centripetal force = m*v^2 / r = m*(r*w)^2 / r = m*w^2*r = 92*800^2*2 = 117760000 N = 117760 kN

(c) t = 27 sec.

angular acceleration, alfa = w / t = 800 / 27 = 29.6 rad/s^2

Angle travelled during this time -

theta = w^2 / (2*alfa) = 800^2 / (2*29.6) = 10800 radians.

Now, 2*pi rad = 360 deg

so, theta = 10800*360 / (2*pi) = 618911 deg.