Converting angle units (degree, radian, revolution)
1. ¼ rev = ….. o (degree) ?
Solution
1 rev = 360o
½ rev = 180o
¼ rev = 90o
2. ½ rev = …….. rad ?
Solution
1 rev = 2π rad = 2(3.14) rad = 6.28 rad
½ rev = pi rad = 3.14 rad
3. 180o = ….. rev ?
Solution
360o = 1 rev
180o = ½ rev
4. 90o = ….. rad ?
Solution
360o = 2π rad = 2(3.14) rad = 6.28 rad
180o = π rad = 3.14 rad
90o = ½ π rad = ½ (3.14) = 1.57
5. 60 rad = ….. rev ?
Solution
6.28 rad = 1 rev
60 rad/6.28 = 9.55 rev
6. 40 rad= ….. o ?
Solution
6.28 rad = 360o
40 rad/6.28 = (6.37)(360o) = 2292.99o
Angular displacement and linear displacement
1. A bike wheel 60 cm in diameter rotates 10 radians. What is the linear displacement of a point on the edge of the wheel?
Known :
Radius (r) = 30 cm = 0.3 m
Angle (θ) = 10 radians
Wanted : linear displacement (l)
Solution :
l = r θ
l = (0.3 m)(10 rad)
l = 3 meters
2. A wheel 50 cm in radius rotates 360o. What is the linear displacement of a point on the edge of the wheel ?
Known :
Radius (r) = 50 cm = 0.5 meters
Angle (θ) = 360o = 6.28 radians
Wanted : linear displacement (l)
Solution :
l = r θ
l = (0.5 m)(6.28 rad)
l = 3.14 meters
3. A wheel 50 cm in radius rotates 2 revolutions. What is the linear displacement of a point on the edge of the wheel ?
Known :
Radius (r) = 50 cm = 0,5 m
Angle (θ) = 2 revolutions = (2)(6.28 radians) = 12.56 radians
Wanted : linear displacement (l) ?
Solution :
l = r θ
l = (0.5 m)(12.56 rad)
l = 6.28 m
4. A point on the edge of a wheel 2 meters in radius, moves 100 meters. Determine the angular displacement.
Known :
Radius (r) = ½ (diameter) = ½ (2 meters) = 1 meter
linear displacement (l) = 100 meters
Solution :
(a) Angular displacement (in radian)
θ = s / r = 100 / 1 = 100 radians
(b) Angular displacement (in degrees)
1 radian = 360o
100 radians = 100(360o) = 36,000 radians
(c) Angular displacement (in revolution)
6.28 radians = 1 revolution
36,000 / 6.28 = 5732,484 revolutions
5. A particle round a circle 10 meters and rotates 180o. What is the radius ?
Known :
Linear displacement (l) = 10 meters
Angle (θ) = 180o = 3.14 radians
Wanted : radius (r)
Solution :
r = l / θ = 10 / 3.14 = 3.18 meters
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