A spoked wheel consists of a thin circular rim of mass and radius connected to a…

PHYSICS · Multi-part · CBSE · Physics · System of Particles and Rotational Motion · System of Particles and Rotational Motion

Problem

A spoked wheel consists of a thin circular rim of mass

m_{\text{rim}}

and radius

R

connected to a light hub by four identical thin uniform spokes, each of length

R

and mass

m_{\text{spoke}}

. The wheel rolls without slipping from rest down a ramp of vertical height

H

. Neglect air resistance. (a) Derive an expression for the wheel’s moment of inertia

I

about its central axis in terms of

m_{\text{rim}}

m_{\text{spoke}}

, and

R

. (b) Using your result from part (a), obtain an expression for the linear speed

v

of the wheel’s center of mass at the bottom of the ramp in terms of

g

H

m_{\text{rim}}

, and

m_{\text{spoke}}

. (c) For

m_{\text{rim}}=2.0\,\text{kg}

m_{\text{spoke}}=0.25\,\text{kg}

R=0.30\,\text{m}

, and

H=1.2\,\text{m}

, calculate the numerical value of

v

. (d) A second wheel has the same total mass as the first but no spokes; all of its mass is concentrated in an identical thin rim. Predict, with justification, whether this second wheel will reach the bottom of the same ramp with a speed that is greater than, less than, or equal to the speed found in part (c).

Related theory

Browse the problem library