Question:
The rotor�s velocity of a helicopter engine changes from $ 330 \,rev/min $ to $ 110 \,rev/min $ in 2 minutes. How long does the rotor blades take to stop?
The rotor�s velocity of a helicopter engine changes from $ 330 \,rev/min $ to $ 110 \,rev/min $ in 2 minutes. How long does the rotor blades take to stop?
Updated On: Aug 20, 2024
- $ 3 \,min $
- $ 4 \,min $
- $ 5 \,min $
- $ 6 \,min $
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The Correct Option is A
Solution and Explanation
Acceleration of helicopter blades
$\alpha = \frac{\omega_2 - \omega_1}{t}$
$\alpha = \frac{330-110}{2}$
$ = 110\,rev/min^2$
Final angular velocity of blades will be zero
i. e., $\omega = 0$
From equation of rotational motion
$\omega = \omega - \alpha t$
$0 = 330 -110 \times t$
$t = 3 \,min$
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Concepts Used:
Motion in a straight line
The motion in a straight line is an object changes its position with respect to its surroundings with time, then it is called in motion. It is a change in the position of an object over time. It is nothing but linear motion.
Types of Linear Motion:
Linear motion is also known as the Rectilinear Motion which are of two types:
- Uniform linear motion with constant velocity or zero acceleration: If a body travels in a straight line by covering an equal amount of distance in an equal interval of time then it is said to have uniform motion.
- Non-Uniform linear motion with variable velocity or non-zero acceleration: Not like the uniform acceleration, the body is said to have a non-uniform motion when the velocity of a body changes by unequal amounts in equal intervals of time. The rate of change of its velocity changes at different points of time during its movement.