Question

A sled attached to a pole by a rope is moving in a circle of radius 3.5.m. it revolves in a complete circle 18 times in 2 minutes. (a) calculate the frequency of the sled's revolution. [2] (b) state its angular frequency.a sled attached to a pole by a rope is moving in a circle of radius 3.5.m. it revolves in a complete circle 18 times in 2 minutes. (a) calculate the frequency of the sled's revolution. [2] (b) state its angular frequency.

Answer 1

The frequency of the sled's revolution is 0.15 rev/s, and its angular frequency is 0.6π rad/s.

Step-by-step explanation:

The frequency of the sled's revolution is calculated by dividing the number of revolutions by the total time in minutes. (a) To find the frequency of the sled's revolution, we use the formula: frequency (f) = number of revolutions / total time. Since the sled completes 18 revolutions in 2 minutes, the frequency is f = 18 rev / 2 min = 9 rev/min. To express this in seconds, since there are 60 seconds in a minute, the frequency is 9 rev/min * (1 min / 60 s) = 0.15 rev/s.

(b) The angular frequency (ω) is related to the frequency by the formula ω = 2π*f. Since the frequency of the sled is 0.15 rev/s, the angular frequency is ω = 2π * 0.15 rev/s. To express the revolution in radians, we use the fact that 1 rev equals 2π radians, hence the angular frequency is ω = 2π * 0.15 * 2π rad/s = 0.15 * 2π² rad/s = 0.15 * 4π rad/s = 0.6π rad/s.