Q. 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)
A.
(1/2)Iω^2
B.
(1/4)Iω^2
C.
(1/3)Iω^2
D.
(1/5)Iω^2
Solution
The rotational kinetic energy is given by K.E. = (1/2)Iω^2.
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 satellite is in a circular orbit around the Earth. What is the relationship between the gravitational force and the centripetal force acting on the satellite? (2022)
A.
Gravitational force > Centripetal force
B.
Gravitational force < Centripetal force
C.
Gravitational force = Centripetal force
D.
No relationship
Solution
For a satellite in a stable orbit, the gravitational force provides the necessary centripetal force, hence they are equal.
Correct Answer:
C
— Gravitational force = Centripetal force
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 at the bottom of the incline? (2021)
A.
√(2gh)
B.
√(3gh/2)
C.
√(gh)
D.
√(4gh/3)
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, mgh = (1/2)mv^2 + (1/5)mv^2, leading to v = √(10gh/7).
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 allowed to fall under gravity. What is the angular acceleration of the rod just after it is released? (2019)
A.
g/L
B.
2g/L
C.
3g/L
D.
g/2L
Solution
The torque τ = Mg(L/2) and moment of inertia I = (1/3)ML². Using τ = Iα, we find α = 3g/2L.
Q. A uniform rod of length L and mass M is pivoted at one end and released from rest. What is the angular velocity 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 is converted to rotational kinetic energy at the bottom. The angular velocity ω can be found using the relation ω = √(3g/L).
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.
Q. A wheel of radius R is rolling without slipping on a horizontal surface. If the wheel has an angular velocity ω, what is the linear velocity of the center of the wheel? (2023)
A.
Rω
B.
ω/R
C.
ω
D.
2Rω
Solution
The linear velocity v of the center of the wheel is given by v = Rω.
Understanding "Mechanics - Rotational Motion" is crucial for students preparing for school and competitive exams. This topic not only forms a significant part of the physics syllabus but also helps in developing a strong conceptual foundation. Practicing MCQs and objective questions enhances your problem-solving skills and boosts your confidence, ensuring you score better in your exams.
What You Will Practise Here
Key concepts of rotational motion, including angular displacement, velocity, and acceleration.
Formulas related to torque, moment of inertia, and angular momentum.
Understanding the relationship between linear and rotational motion.
Diagrams illustrating rotational dynamics and equilibrium.
Important definitions such as centripetal force and angular frequency.
Application of theorems like the parallel axis theorem and perpendicular axis theorem.
Problem-solving techniques for various types of rotational motion scenarios.
Exam Relevance
The topic of "Mechanics - Rotational Motion" is frequently featured in CBSE, State Boards, NEET, and JEE exams. Students can expect questions that test their understanding of concepts, numerical problems, and application-based scenarios. Common question patterns include direct MCQs, assertion-reason type questions, and numerical problems requiring the application of formulas.
Common Mistakes Students Make
Confusing linear and angular quantities, such as mixing up linear velocity with angular velocity.
Neglecting the direction of torque and angular momentum in problems.
Misapplying formulas, especially in problems involving multiple objects or systems.
Overlooking the significance of the moment of inertia in rotational dynamics.
FAQs
Question: What is the moment of inertia? Answer: The moment of inertia is a measure of an object's resistance to changes in its rotational motion, depending on the mass distribution relative to the axis of rotation.
Question: How is torque calculated? Answer: Torque is calculated using the formula τ = r × F, where τ is torque, r is the distance from the pivot point to the point of force application, and F is the applied force.
Ready to enhance your understanding of "Mechanics - Rotational Motion"? Dive into our practice MCQs and test your knowledge today! Mastering these concepts will not only prepare you for exams but also build a strong foundation in physics.
Soulshift Feedback×
On a scale of 0–10, how likely are you to recommend
The Soulshift Academy?
