Q. A flywheel is rotating with an angular velocity of 10 rad/s. If the moment of inertia of the flywheel is 2 kg·m², what is its rotational kinetic energy? (2020)
A.100 J
B.50 J
C.20 J
D.10 J
Solution
Rotational kinetic energy K.E. = (1/2)Iω² = (1/2)(2)(10)² = 100 J.
Q. A rotating body has an angular momentum L. If its moment of inertia is doubled and angular velocity is halved, what will be the new angular momentum? (2021)
Q. A solid cylinder and a hollow cylinder of the same mass and radius are released from rest at the same height. Which one reaches the ground first? (2022)
A.Solid cylinder
B.Hollow cylinder
C.Both reach at the same time
D.Depends on the height
Solution
The solid cylinder has a lower moment of inertia, thus it accelerates faster and reaches the ground first.
Q. A solid sphere of mass M and radius R rolls without slipping down an inclined plane of height h. What is the speed of the center of mass of the sphere when it reaches the bottom? (2021)
A.√(2gh)
B.√(5gh/7)
C.√(3gh/5)
D.√(gh)
Solution
Using conservation of energy, potential energy at the top = kinetic energy at the bottom. The total kinetic energy is the sum of translational and rotational kinetic energy. Thus, v = √(5gh/7).
Q. A uniform rod of length L and mass M is pivoted at one end and released from rest. What is the angular speed of the rod just before it hits the ground? (2019)
A.√(3g/L)
B.√(2g/L)
C.√(g/L)
D.√(4g/L)
Solution
Using conservation of energy, potential energy at the top converts to rotational kinetic energy at the bottom. The angular speed ω = √(3g/L).
Q. A wheel of radius R and mass M is rolling without slipping on a horizontal surface. If it has a linear speed v, what is its total kinetic energy? (2022)
A.(1/2)Mv²
B.(1/2)Mv² + (1/2)(Iω²)
C.(1/2)Mv² + (1/2)(Mv²)
D.(1/2)Mv² + (1/2)(Mv²/2)
Solution
The total kinetic energy is the sum of translational and rotational kinetic energy. K.E. = (1/2)Mv² + (1/2)(Iω²) where I = (1/2)MR² for a solid cylinder.
