Angular Speed

Question 1: 10 kg mass is moving in circular path of radius 5m, completes one round in 4 seconds. Calculate the linear speed and angular speed of mass.Solution: m = 10kg, r = 5m and t = 4 seconds, V = ?

Linear speed, V = 2πrt  = 2 x 3.14 x 54

V = 7.85 m/s

Now, ω = Vr = 7.855 = 1.57 rad. /s

Question 2: Calculate the angular speed of an hour hand.Solution: Angular distance = 2 π & T = 12 hours = 12 x 60 x 60 s = 43200 s (this is the time for one complete circular motion)

Now, ω =  2πt  = 2 x 3.1443200  = 1.45 x 10−4 rad. /s

 Question 3: What is the angular speed of earth of rotation of earth on its axis?Solution: Angular distance = 2 π = 2 x 3.14 = 6.28 rad.

       Time period (T) = 24 hours = 24 x 60 x 60 = 86400 s

      Now, ω = 2πt = 6.886400 = 7.27 x 10−5 rad. /s

 Question 4: A wheel of 0.60m in radius is moving with a speed of 10m/s. Find the angular speed.Solution: r = 0.60m and V = 10m/s

Now, ω = Vr = 100.60 = 16.67 rad./s

 Question 5: The angular speed of wheel is 88 rad./s. Calculate the number of revolutions made by it in one second.Solution: ω = 88 rad./s

1 rad./s = (12π) rev. /s

88 rad./s = 88(2×227) rev./s = 14 rev/s.

 

Marie Rose Domingo

III- St. Ignatius of Loyola