Question

A record turntable is rotating at 33 1 3 rev/min. a watermelon seed is on the turntable 5.0 cm from the axis of rotation. (a) calculate the acceleration of the seed, assuming that it does not slip. (enter the magnitude.)

Answer 1

Since the motion is rotational, we can associate this with centrifugal/centripetal acceleration. The formula for this is:

a = v²/r = (rω)²/r = rω²
where ω is the angular velocity and r is the radius

Let's convert v in terms of rad/min. The conversion from rev to rad is, 1 rev = 360° = 2π. So,
ω = 33 1/3 rev/min * 2π rad/1 rev = 209.44 rad/min

a = 5 cm(209.44 rad/min)²
a = 219,325.568 cm/min²

Answer 2

Distance D = 5 cm = 0.05m
Revolutions = 33.33 per min => t = 60 sec
Acceleration is v^2 / r, so first we need to find velocity
Velocity = (D x 3.14 x r) / t => (0.05 x 3.14 x 33.33) / 60
Velocity = 0.0872 m/s
Acceleration = v^2 / r = 0.0872^2 / 0.05 = 0.152.