WebSuppose a ball is rolling without slipping on a surface ( with friction) at a constant linear velocity. We know that there is friction which prevents the ball from slipping. Why doesn't this frictional force act as a torque and speed up the ball as well?The force is present. It can act as a torque. http://complex.gmu.edu/www-phys/phys705/notes/007%20Examples%20Constraints%20and%20Lagrange%20Equations.pdf
Chapter 2 Rolling Motion; Angular Momentum
WebNow, for rotational motion : For no skidding Vp = 0. Therefore, As a result, For the case of rolling without slipping, this is the equation relating the velocity of the geometric center of the wheel O to the angular velocity w … WebLooking at the equation: Kr = (1/2) * m * r^2 * ω^2. Without the summation portion this is the rotational kinetic energy of a small piece of the object. The term r is not the radius of the whole object. It is the distance of the small part of the object we are looking at is away from the axis of rotation. fbd2400kb10b
11.1 Rolling Motion - University Physics Volume 1
WebA sphere is rolling without slipping on a horizontal plane. The plane is itself rotating at constant angular velocity . We have three vector equations: Newton’s equations for linear and angular acceleration, and the rolling condition. We want to find the path taken by the rolling ball on the rotating surface, that is, . WebJun 6, 2011 · Homework Equations All the usually relevant circular motion equations involving θ, I, ⍺, τ and ω The Attempt at a Solution I've tried to work from the energy of the cylinder (Using E k = K trans + K rot) and equating the energy to its potential energy at the point it starts to roll down but got nowhere near the answer.I've done the force diagram, … WebOnce we know what a is, this gives the minimum friction necessary to keep the cylinder rolling without slipping. Substituting this into our first equation gives Ma = Mg sin θ - Ia/R 2, or a = g sin θ - Ia/MR 2, which rearranges to a(1 + I/MR 2) = g sin θ, which then gives a = g sin θ/(1 + I/MR 2). hopeman gc