Question

Find the tangential velocity and centripetal acceleration of a particle glued to the tip of a fan blade which has a radius of 20cm and rotate at an angular frequency of 100r.p.m

Answer 1

Tangential velocity, V=wr

r=radius, w=angular velocity

w=2πf

[F is frequency which 100]

w=2×3.14×100

=628rads/s

Given that the radius,r is 20cm 0.2m substituting in V=wr

V=628×0.2

V=125.6m/s

R= 20cm= 0.2m

ω= 100 rev= 100 × 2π rad = 200π rad

v= Rω = 0.2 × 200π = 40π m/s= 125.66m/s

ac= v²/R = (40π)²/0.2 = 8000π² m/s²= 78956.84m/s²