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Published on: 29/08/2019
System of Particles and Rotational Motion
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1.
A constant torque of 120 N-m rotates its point of action by an angle of 30\(^{o}\). What is the work done by the torque?
2.
What is the moment of inertia of a sphere of mass 20 kg and radius \(\frac { 1 }{ 4 } \) m about its diameter?
3.
About which axis would a uniform cube have a minimum rotational inertia?
4.
Does the radius of gyration depend upon the speed of rotation of the body?
5.
In a flywheel, most of the mass is concentrated at the rim. Explain why?
6.
Two solid spheres of the same mass are made of metals of different densities. Which of them has a larger moment of inertia about the diameter?
7.
Does the moment of inertia of a rigid body change with the speed of rotation?
8.
Why is moment of inertia also called rotational inertia?
9.
A particle is moving on the x-axis with a linear velocity of 2 m/s. What will be its angular momentum about the origin?
10.
A ball is moving with a velocity of 10m/s. Suddenly, it breaks into two equal parts. What will be the speed of centre of mass of the system after explosion?
1.
Work done by the torque, W = tθ
\(= 120 \times (\frac{30 \times \pi}{180})=20πJ.\)
2.
Moment of inertia of a sphere about its diameter,
\(I=\frac{2}{5} m R^2=\frac{2}{5} \times 20 \times\left(\frac{1}{4}\right)^2=0.5 \mathrm{~kg}-m^2 .\)
3.
In a uniform cube, the mass is more concentrated about a diagonal.
4.
No, it depends only on the distribution of mass of the body.
5.
Concentration of mass at the rim increases the moment of inertia and thereby brings uniform motion.
6.
The sphere with smaller density will larger radius and hence larger moment of inertia.
7.
No. because the moment of inertia depends upon the axis of rotation and distribution of mass.
8.
The moment of inertia gives a measure of inertia in rotational motion. So, it is also called rotational inertia.
9.
Zero
10.
10 m/s
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