Answer:
a) The angular velocity is 0.4π radians/second ⇒1.25664 radians/second
b) The wheel travels 124.4071 meters in 5 minutes ⇒ 39.6π meters
Explanation:
The angular velocity ω = 2 π n ÷ t, where
- n is the number of revolution
The distance that moving by the angular velocity is d = ω r t, where
- r is the radius of the circle in meter
a)
∵ A wheel completes 12 revolutions in 1 minute
∴ n = 12
∴ t = 1 minute
→ Change the minute to seconds
∵ 1 minute = 60 seconds
∴ t = 60 seconds
→ Substitute n and t in the rule above
∵ ω = 2 (π) (12) ÷ 60
∴ ω = 24π ÷ 60
∴ ω = 0.4π radians/second
∴ The angular velocity is 0.4π radians/second ⇒1.25664 radians/second
b)
→ To find the distance in 5 minutes multiply ω by the radius by the time
∵ The wheel has a radius of 33 cm
∴ r = 33 cm
→ Change it to meter
∵ 1 m = 100 cm
∴ r = 33 ÷ 100 = 0.33 m
∵ t = 5 minutes
→ Change it to seconds
∴ t = 5 × 60 = 300 seconds
→ Substitute them in the rule of the distance above
∵ d = 0.4π (0.33) (300)
∴ d = 39.6π meters ⇒ 124.407 meters
∴ The wheel travels 124.4071 meters in 5 minutes ⇒ 39.6π meters