# 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

3. 180o = ….. rev ?

Solution

360o = 1 rev

180o = ½ rev

[irp]

4. 90o = ….. rad ?

Solution

90o = ½ π rad = ½ (3.14) = 1.57

5. 60 rad = ….. rev ?

Solution

6. 40 rad= ….. o ?

Solution

40 rad/6.28 = (6.37)(360o) = 2292.99o

[irp]

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

Wanted : linear displacement (l)

Solution :

l = r θ

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 = 3.14 meters

[irp]

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

Wanted : linear displacement (l) ?

Solution :

l = r θ

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 :

θ = s / r = 100 / 1 = 100 radians

(b) Angular displacement (in degrees)

(c) Angular displacement (in revolution)

36,000 / 6.28 = 5732,484 revolutions

[irp]

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