$A$ wheel in uniform motion about an axis passing through its centre and perpendicular to its plane is considered to be in mechanical (translational plus rotational) equilibrium because no net external force or torque is required to sustain its motion. However,the particles that constitute the wheel do experience a centripetal acceleration directed towards the centre. How do you reconcile this fact with the wheel being in equilibrium?
How would you set a half wheel into uniform motion about an axis passing through the centre of mass of the wheel and perpendicular to its plane? Will you require external forces to sustain the motion?

Vedclass pdf generator app on play store
Vedclass iOS app on app store
(N/A) wheel is a rigid body. The particles of the wheel experience centripetal acceleration directed towards the centre. This acceleration is provided by internal elastic forces (tensions),which cancel out in pairs due to Newton's third law. Since the net external force and net external torque are zero,the wheel is in mechanical equilibrium.
In a half wheel,the distribution of mass about its centre of mass (through which the axis of rotation passes) is not symmetrical. Therefore,the direction of the angular momentum vector of the wheel does not coincide with the direction of its angular velocity vector. As the wheel rotates,the angular momentum vector changes direction,which requires a non-zero external torque. Hence,external forces and torques are required to sustain the motion of the half wheel.

Explore More

Similar Questions

$A$ car weighs $1800 \; kg$. The distance between its front and back axles is $1.8 \; m$. Its centre of gravity is $1.05 \; m$ behind the front axle. Determine the force exerted by the level ground on each front wheel and each back wheel.

Difficult
View Solution

State the principle of moments for a lever.

$A$ uniform rod of mass $15\,kg$ and length $5\,m$ is held stationary with the help of a light string as shown. The tension in the string is ......... $N.$

In an experiment with a beam balance,an unknown mass $m$ is balanced by two known masses of $16\, kg$ and $4\, kg$ as shown in the figure. The value of the unknown mass $m$ is ....... $kg$.

Difficult
View Solution

As shown in the figure,a person holds a book between their finger and thumb (the book is held at the corner). If the weight of the book is $W$,what is the torque exerted by the person on the book?

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial
For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free
For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo