StemCET Logo

Physics Question 28 – JEE-MAIN 2025

← Back
A wheel is rolling on a plane surface. The speed of a particle on the highest point of the rim is 8 m/s. The speed of the particle on the rim of the wheel at the same level as the centre of wheel, will be :

Understand that the velocity of any point on a rolling wheel is the vector sum of the translational velocity of the center of mass and the rotational velocity relative to the center.

🥷
Ninja Strategy•Vector Addition for Rolling Motion

Recognize that the velocity of points on the rim is a vector sum of translational and rotational components, and for points at the center's level, these components are perpendicular.

Step 1: Determine the velocity of the center of mass (vc).✦ Active

For a wheel rolling without slipping, the velocity of the highest point (vtop) is twice the velocity of the center of mass (vc). Given vtop=8 m/s.

vtop=2vc⟹8 m/s=2vc⟹vc=4 m/s

For rolling without slipping, the tangential speed due to rotation is equal to the speed of the center of mass, so ωR=vc=4 m/s.

Step 2: Calculate the velocity of a point at the same level as the center.○ Expand

Consider a point on the rim at the same horizontal level as the center. The velocity of this point is the vector sum of the translational velocity of the center of mass (vc→) and the tangential velocity due to rotation (vt→). At these points, vc→ is horizontal and vt→ is vertical (magnitude ωR). Since they are perpendicular, the magnitude of the resultant velocity is vside=vc2+vt2.

Step 3: Substitute values and find the final speed.○ Expand

Using vc=4 m/s and vt=ωR=4 m/s:

vside=(4 m/s)2+(4 m/s)2=16+16=32=42 m/s
✦ STEM Console utilizes AI models to generate step-by-step explanations and math clues. AI can make mistakes.