Question

The blades of an aeroplane propeller are rotating at the rate of 600 revolutions per minute. Its angular velocity is
(A) \[20\pi \dfrac{{rad}}{s}\]
(B) \[10\pi \dfrac{{rad}}{s}\]
(C) \[2\pi \dfrac{{rad}}{s}\]
(D) \[\pi \dfrac{{rad}}{s}\]

Answer 1

Hint: In this question we will calculate the angular velocity of the blades of an aeroplane propeller. For this we first calculate the angle the blades of an aeroplane propeller covers in 600 revolutions.
To calculate this we first calculate the angle covered in 1 revolution and then find the angle covered in 600 revolution in one minute.
Then we will use the formula of angular velocity i.e. \[\omega = \dfrac{\theta }{t}\] to calculate the angular velocity of the blades of an aeroplane propeller and after solving this result we will find the correct option.

Complete step by step answer
Angular velocity i.e. ‘ \[\omega \] ’ is said to be the rate of the velocity at which an object is rotating around in a specific point in a given time or at centre.
We have to calculate the angular velocity of blades of an aeroplane propeller. We have given that blades of an aeroplane propeller are rotating at 600rpm, which means the blades are rotating 600 rotations in one minute.
Now to calculate the angular velocity of the blades of the aeroplane propeller, we have to calculate the angle the blades cover in 600 revolutions.
So, we calculate the angle covered in 600 revolutions as:
Blades are rotating at the rate 600rpm
So, the angle the blades are covering in 1 revolution \[ = 2\pi \]
Then angle covered by the blades of the aeroplane in 600 revolutions \[\; = 600 \times 2\pi = 1200\pi \] rad
We know that the time taken for 600 revolutions = 1 minute and 1 minute = 60 seconds.
Also, we know that the angular velocity of an object in circular motion:
 \[\omega = \dfrac{\theta }{t}\] , where \[\omega \] is the angular velocity, \[\theta \] is the angle covered and t is the time taken.

So, after putting in the values we get \[\omega = \dfrac{{1200\pi rad}}{{60s}}\]
After solving we get the value of angular velocity i.e. \[\omega = 20\dfrac{{rad}}{s}\] .

So, option A is correct.

Note: Remember that the formula of velocity of an object in linear motion and velocity of a particle in circular motion are same where in linear velocity we have \[v = \dfrac{d}{t}\] and in angular velocity we have \[\omega = \dfrac{\theta }{t}\] .
Also remember that in the case of circular motion we have angular acceleration where \[\alpha \] is constant and also have 3 motion equations similar to linear motion equations.
Always keep in mind that what is the SI unit of the thing we are calculating and proceed according to that. As in this case we have to calculate angular velocity whose SI unit is \[\dfrac{{rad}}{s}\] . That’s why we changed the minute to second, otherwise our answer gets wrong.