Question:
A string is wound round the rim of a mounted flywheel of mass 20 kg and radius 20 cm. A steady pull of 25 N is applied on the cord. Neglecting friction and mass of the string, the angular acceleration of the wheel is
A string is wound round the rim of a mounted flywheel of mass 20 kg and radius 20 cm. A steady pull of 25 N is applied on the cord. Neglecting friction and mass of the string, the angular acceleration of the wheel is
Updated On: Oct 4, 2023
- 50 $\,s^{-2}$
- 25 $\,s^{-2}$
- 12.5 $\,s^{-2}$
- 6.25 $\,s^{-2}$
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The Correct Option is C
Solution and Explanation
The mass of flywheel = 20 kg
Radius = 20 cm
= $\frac{20}{100} m = \frac{1}{5}m$
The moment of inertia = $\frac{1}{2}MR^2 = \frac{1}{2} \times 20 \times \frac{1}{5}$
I = 0.4 $kg-m^2$
Angular acceleration $\alpha = \frac{\tau}{I} $
= $\frac{FR}{I} = \frac{25 \times \frac{1}{5}}{0.4} =12.5 s^{-2}$
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Concepts Used:
Motion in a Plane
It is a vector quantity. A vector quantity is a quantity having both magnitude and direction. Speed is a scalar quantity and it is a quantity having a magnitude only. Motion in a plane is also known as motion in two dimensions.
Equations of Plane Motion
The equations of motion in a straight line are:
v=u+at
s=ut+½ at2
v2-u2=2as
Where,
- v = final velocity of the particle
- u = initial velocity of the particle
- s = displacement of the particle
- a = acceleration of the particle
- t = the time interval in which the particle is in consideration