3 questions about Angular velocity equation
1. An object moving in a circular path has a radius of 0.5 m. The particle is able to cover an angle of 60π rad in 15 seconds. Determine the angular speed of the object.
Known:
Radius (r) = 0.5 meters
Angle (θ) = 60π rad
Time interval (t) = 15 seconds
Wanted: Angular velocity (ω)
Solution:
θ = ω t
60π = ω (15)
ω = 60π / 15 = 4π rad/s
2. A bicycle wheel with a radius of 30 cm rotates at a constant speed. The tire valve can rotate at an angle of 120π rad for 10 seconds. Determine the angular speed.
Known:
Radius (r) = 30 cm
Angle (θ) = 120π rad
Time interval (t) = 10 s
Wanted: Angular velocity (ω)
Solution:
θ = ω t
120π = ω (10)
ω = 120π / 10 = 12π rad/s
3. The rope is wrapped around a wheel with radius R = 25 cm as shown. If a point on the rope (point A) has a speed of 5 m/s then the rotational speed of the wheel is…
Known:
Radius (r) = 25 cm = 0.25 meters
Speed (v) = 5 m/s
Wanted: Angular velocity (ω)
Solution:
The formula for the relation between angular speed, linear speed and radius:
v = r ω
5 = (0,25) ω
ω = 5 / 0,25 = 20 rad/s
