Question

An ant sits on a cd at a distance of 17 cm from the center. If it sits there for 42

seconds, it travels a total distance of 913 cm.
a)
How many rotations did the ant make?
b)
What speed has the ant been traveling at? (in cm/see)
c)
What is the period of the ant's revolutions? (in s)
d)
What rotational speed is the cd turning at? (in rpm)

Answer 1

a) N = 8.54[rev]; b) v = 21.73 [m/s]; c) T = 4.918[s]; d) 12.2[rev/min]

Step-by-step explanation:

We know that the arc length is calculated by the following expression:

L = α * r

where:

r = radius = 17 [cm] or 0.17 [m]

α = 360° or 2*pi [rad] = 6.283 [rad]

L = (6.283*0.17) = 1.068 [m] = 106.81 [cm] is the distance travelled in one revolution of the CD

a) N = number of revolutions

N = 913 / 106.81

N = 8.54 [rev]

b ) The speed can be calculated by the following expression:

v = d/t

Where:

d = distance = 913[cm]

t = time = 42[sec]

v = 913/42 = 21.73 [cm/s]

c)

We have the number of revolutions and the time therefore we can calculate the number of revolutions per second

w = 8.54 / 42 =0.2033 [rev/s]

And we know that the period is the reciprocal of the time

T = 1 / 0.2033

T = 4.918 [s]

d )

We need to convert from [rev/s] into [rev/min]

`0.2033[(rev)/(s)]*60[(s)/(1min)]\\12.198[rev/min]`