Question

An automatic clothing drier spins at 51.6 rev/min. If the radius of the drier drum is 30.5 cm, how fast (in m/s) is the drier drum moving.

Answer 1

Given info : An automatic clothing drier spins at 51.6 rev/min. if the radius of the drier drum is 30.5 cm.

To find : How fast (in m/s ) is the drier drum moving ?

solution : An automatic clothing drier spins in circular motion. and we know, if any particle is moving in circular motion it follows v = ωr

where v is linear velocity, ω is angular velocity and r is the radius of circle in which particle moves.

here, angular velocity, ω = 51.6 rev/min

1 rev/min = 2π/60 rad/s = π/30 rad/s

so ω = 51.6 × π/30 = 51.6 × 3.14/30 rad/s = 5.4008 rad/s

radius , r = 30.5 cm = 0.305 m

now v = 5.4008 rad/s × 0.305 m ≈ 1.65 m/s

Therefore drier drum is moving with 1.65 m/s speed.