Answer to Question #97695 in Mechanics | Relativity for Shaina M Simmonds

Question

1. A disk with a diameter of 18 cm is spun at a constant rate. The disk rotates 9 times every 1.3 seconds
a) What are the frequency and period of rotation?
b) What is the angular velocity in radians/sec?
c) What is the tangential velocity of a point on the edge of the disk?

Answer 1

a) Frequency of rotation, f

$$f=\frac{9 cycles}{1.3 seconds} = 6.9\frac{cycles}{second} = 6.9 Hz$$

Period of rotation, T

$$T =\frac{1}{f} = \frac {1}{6.9 Hz} = 0.14 s$$

b) Angular velocity, ω

$$ω = 2πf = 2\times 3.14\times 6.9 Hz = 43 \frac {radians}{sec}$$

c) tangential velocity of a point on the edge of the disk, ν

$$ν=ωr = ω\times \frac {d}{2} = 43 \frac {radians}{sec}\times\frac{18 cm}{2} = 387 \frac{cm}{s}$$