Question

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

Answer 1

Answer:

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

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]

$0.2033[\frac{rev}{s}]*60[\frac{s}{1min}]\\12.198[rev/min]$