Rolling Motion

topicmedium9 MCQ

Rolling without slipping, kinetic energy sharing and motion on an incline. (Physics › System of Particles and Rotational Motion, NEET UG syllabus.)

Practice 9 questions Back to syllabus~14 min

What is Rolling Motion?

A type of motion that is a combination of translational motion of the center of mass and rotational motion about an axis passing through the center of mass.

Key formula / rule: Condition for Rolling without Slipping

Key points

Define rolling motion and distinguish between rolling with and without slipping.
Relate linear and angular velocities for rolling without slipping.
Calculate the total kinetic energy of a rolling body.
Analyze the motion of a body rolling down an inclined plane.

Common exam trap

Confusing static friction with kinetic friction in rolling without slipping. Static friction acts, but does no work.

Definitions

Term: Rolling Motion
Meaning: A type of motion that is a combination of translational motion of the center of mass and rotational motion about an axis passing through the center of mass.

Term: Rolling without Slipping
Meaning: An ideal rolling motion where the point of contact between the rolling body and the surface is instantaneously at rest relative to the surface, implying no relative motion or friction losses at that point.

Term: Instantaneous Axis of Rotation
Meaning: For a body rolling without slipping, it is the axis passing through the point of contact and perpendicular to the plane of motion, about which the body can be considered to be purely rotating at that instant.

Learning objectives

Define rolling motion and distinguish between rolling with and without slipping.
Relate linear and angular velocities for rolling without slipping.
Calculate the total kinetic energy of a rolling body.
Analyze the motion of a body rolling down an inclined plane.
Determine the acceleration and final velocity of rolling bodies on an incline.
Apply conservation of energy principles to rolling motion problems.

Formulae

Name: Condition for Rolling without Slipping
Note: Relates linear velocity of center of mass (v_CM) to angular velocity (ω) and radius (R) for ideal rolling.
Expression: v_CM = Rω

Name: Total Kinetic Energy of a Rolling Body
Note: Sum of translational kinetic energy and rotational kinetic energy about the center of mass.
Expression: KE_total = 1/2 mv_CM^2 + 1/2 I_CM ω²

Name: Total Kinetic Energy (alternative form)
Note: Derived by substituting ω = v_CM/R into the total KE formula.
Expression: KE_total = 1/2 mv_CM^2 (1 + I_CM / (mR²))

Name: Acceleration of a Body Rolling Down an Inclined Plane
Note: 'g' is acceleration due to gravity, 'θ' is the angle of inclination. I_CM is moment of inertia about CM, 'm' is mass, 'R' is radius.
Expression: a = (g sinθ) / (1 + I_CM / (mR²))

Name: Moment of Inertia (I_CM) for Ring/Hollow Cylinder
Note: About an axis passing through its center and perpendicular to its plane.
Expression: I_CM = mR²

Name: Moment of Inertia (I_CM) for Disc/Solid Cylinder
Note: About an axis passing through its center and perpendicular to its plane.
Expression: I_CM = 1/2 mR²

Name: Moment of Inertia (I_CM) for Solid Sphere
Note: About any diameter.
Expression: I_CM = 2/5 mR²

Name: Moment of Inertia (I_CM) for Hollow Sphere
Note: About any diameter.
Expression: I_CM = 2/3 mR²

Prerequisites

Translational motion (kinematics and dynamics).
Rotational motion (angular displacement, velocity, acceleration, torque, moment of inertia, rotational kinetic energy).
Conservation of energy.
Newton's laws of motion.
Understanding of friction (static and kinetic).

Common mistakes

Confusing static friction with kinetic friction in rolling without slipping. Static friction acts, but does no work.
Forgetting to include both translational and rotational kinetic energy in total KE calculations.
Incorrectly applying v = Rω when slipping occurs.
Assuming acceleration on an incline is g sinθ for rolling bodies (it's only for pure sliding).
Using the wrong moment of inertia for a given shape.
Not understanding that the point of contact is instantaneously at rest.

Keywords

Rolling
Slipping
Translational Kinetic Energy
Rotational Kinetic Energy
Moment of Inertia
Inclined Plane
Angular Velocity
Linear Velocity
Center of Mass
Static Friction

Practice preview

For a rigid body of radius R undergoing pure rolling motion with a linear velocity v of its center of mass, what is the relation between v and its angular velocity ω?…
easy
A solid sphere, a hollow sphere, and a disc, all of the same mass and radius, roll without slipping down an inclined plane from rest. Which one will reach the bottom first?…
medium
A solid sphere rolls without slipping down an inclined plane. If the coefficient of static friction between the sphere and the plane is μ_s, what is the minimum value of μ_s required for pure rolling to occur?…
hard

Practice 9 questions