Free Angular Displacement MCQs with Answers

1. One radian is defined as the angle subtended at the centre of a circle by an arc whose length is

• A. equal to the radius
• B. equal to the diameter
• C. equal to the circumference
• D. one metre

Explanation: Since the arc length equals the radius times the angle in radians, an arc of one radius length subtends exactly one radian, about 57.3 degrees. A full circle is therefore 2 pi radians, because the circumference is 2 pi times the radius. Defining the angle this way is what makes the arc length formula and the link between linear and angular quantities so simple.

2. An angle of 180 degrees expressed in radians is

• A. pi over 2
• B. pi
• C. 2 pi
• D. 3 pi over 2

Explanation: A complete revolution of 360 degrees is 2 pi radians, so half a revolution is pi radians, roughly 3.14. A quarter turn of 90 degrees is pi over 2. Converting between the two is simply multiplying by pi over 180 in one direction and by 180 over pi in the other.

3. Angular displacement is measured in

• A. metres
• B. radians
• C. metres per second
• D. newtons

Explanation: The radian is the SI unit of angle, and because it is defined as a ratio of two lengths it is dimensionless, which is why the formula v equals r omega comes out in metres per second without any conversion factor. Degrees and revolutions are convenient in practice but must be converted to radians before use in these formulae. Linear displacement, by contrast, is measured in metres.

4. An angular displacement of 90 degrees is equal to:

• A. One-fourth revolution
• B. One-third revolution
• C. One half revolution
• D. One complete revolution

Explanation: A full revolution is 360 degrees, so 90 degrees is a quarter of it, equivalent to pi over 2 radians. Half a revolution would be 180 degrees or pi radians. Converting between degrees, radians and revolutions is worth doing fluently, since rotational formulae require radians.