Q1. What is the angular momentum of a particle of mass 2 kg moving in a circle of radius 3 m with a speed of 4 m/s? (2021)
Solution:
Angular momentum L = mvr, where v is the tangential speed. L = 2 kg * 4 m/s * 3 m = 24 kg·m²/s.
⏱ Time: 0s
Q2. A flywheel is a device used to store rotational energy. If the moment of inertia of the flywheel is I and it rotates with an angular velocity ω, what is its rotational kinetic energy? (2020)
Solution:
The rotational kinetic energy is given by K.E. = (1/2)Iω^2.
⏱ Time: 0s
Q3. 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)
Solution:
Using conservation of energy, potential energy at the top converts to rotational kinetic energy at the bottom. The angular speed ω = √(3g/L).
⏱ Time: 0s
Q4. A disc of radius R and mass M is rotating about its axis with an angular velocity ω. What is the moment of inertia of the disc? (2020)
Solution:
The moment of inertia of a solid disc about its central axis is given by I = (1/2)MR².
⏱ Time: 0s
Q5. A torque τ is applied to a rigid body with a moment of inertia I. If the torque is doubled, what happens to the angular acceleration? (2019)
Solution:
According to Newton's second law for rotation, τ = Iα. If τ is doubled, α also doubles.
⏱ Time: 0s
Q6. 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)
Solution:
The solid cylinder has a lower moment of inertia, thus it accelerates faster and reaches the ground first.
⏱ Time: 0s
Q7. If the radius of a rotating object is halved while keeping the angular velocity constant, what happens to its linear velocity? (2022)
Solution:
Linear velocity v = rω, so if r is halved and ω remains constant, v also halves.
⏱ Time: 0s
Q8. A disk and a ring of the same mass and radius are rolling down the same incline. Which one has a greater acceleration? (2019)
Solution:
The disk has a smaller moment of inertia than the ring, resulting in greater acceleration down the incline.
⏱ Time: 0s
Q9. 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)
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).
⏱ Time: 0s
Q10. A wheel is rotating with an angular acceleration of 2 rad/s². If it starts from rest, what will be its angular velocity after 5 seconds? (2022)
Solution:
Using the formula ω = ω₀ + αt, where ω₀ = 0, α = 2 rad/s², and t = 5 s, we get ω = 0 + 2*5 = 10 rad/s.
