Question

A phonograph record 30.48 cm in diameter roatates 33 1/3 revolutions per minute. Calculate:

a) The linear speed of a speck of dust on the rim of the record

b) The centripetal acceleration of the speck of dust

Answer 1

a)

linear speed = angular speed x radius of the rotation

v = ωr

v = linear speed (m/s)

ω = angular speed (radians/s) = 3.5 rad/sec

r = radius of the rotation (m) = 0.1524 cm

v = 3.5*0.1524 = 0.53m/s

b)

Centripetal acceleration for uniform circular motion is defined as
a = v^2 / r
Where v is the tangential velocity of a point on the edge of the circle, and r is the radius.

the formula for the circumference of a circle = 2πr

diameter, d = 30.48cm <==> radius, r = 15.24cm
v = 33 1/3rev/min = 33 1/3rev*(2πr / rev)/min = 21.78πr/min

So, a = (474.38*3.14*3.14*15.24)

a = 7.128m/s².