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Angular displacement and linear displacement – problems and solutions

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

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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

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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

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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

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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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  1. Converting angle units sample problems with solutions
  2. Angular displacement and linear displacement sample problems and solutions
  3. Angular velocity and linear velocity sample problems with solutions
  4. Angular acceleration and linear acceleration sample problems with solutions
  5. Uniform circular motions sample problems with solutions
  6. Centripetal acceleration sample problems with solutions
  7. Nonuniform circular motions sample problems with solutions

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