Rolling without slipping couples translation and rotation, v=ωr.
Rolling without slipping requires v=ωr at the contact point, which has zero velocity. Kinetic energy is ½mv²+½Iω². Rolling resistance arises from deformation, which is far smaller than sliding friction.
A solid sphere rolls down a slope at 5/7 g sinθ.
Rolling without slipping links translation and rotation, so it is central to wheel, ball and gear analysis.
Rolling without slipping couples translation and rotation, v=ωr.
Rolling without slipping links translation and rotation, so it is central to wheel, ball and gear analysis.
Some of the energy goes into rotation, so less is available for linear motion, which reduces the translational acceleration.
The contact point has zero velocity, so the centre velocity equals angular speed times radius.
Typical applications include finding the speed of a car from wheel rotation, calculating the acceleration of a solid ball rolling down a ramp and checking the traction needed for a wheel to drive a vehicle without slipping.
Study "Gyroscopic effects" first (topic 39 of 106 in Engineering Mechanics). It covers the groundwork this topic builds on.
Contact point is the instantaneous centre. Acceleration down an incline a=g sinθ/(1+I/mr²). Static friction does no work.
A solid sphere rolls down a slope at 5/7 g sinθ.
The next topic is "Circular motion and centripetal force", which builds directly on this one.
It is classed as Intermediate in Engineering Mechanics (topic 40 of 106). It is an intermediate topic. Work through the beginner topics in Engineering Mechanics first.
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