A disk of radius R and mass m is rolling down an inclined plane at an angle a. The coefficient of static friction between the R inclined plane and the disk is µs. The disk rolls without slipping sufficiently high; however, the disk will begin to slip for µs below a certain threshold. (a) Assuming that there is no slipping, list down the Lagrangian equations of motion. Include the constraint forces at the point of contact and use the coordinate axis indicated on the figure on the right. (b) What is the value of µs at which the disk would begin to slip? if us becomes a
A disk of radius R and mass m is rolling down an inclined plane at an angle a. The coefficient of static friction between the R inclined plane and the disk is µs. The disk rolls without slipping sufficiently high; however, the disk will begin to slip for µs below a certain threshold. (a) Assuming that there is no slipping, list down the Lagrangian equations of motion. Include the constraint forces at the point of contact and use the coordinate axis indicated on the figure on the right. (b) What is the value of µs at which the disk would begin to slip? if us becomes a
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Transcribed Image Text:2. A disk of radius R and mass m is rolling
down an inclined plane at an angle a. The
coefficient of static friction between the
R
inclined plane and the disk is µs. The disk
rolls without slipping if Hs becomes
sufficiently high; however, the disk will
begin to slip for µs below a certain threshold.
(a) Assuming that there is no slipping, list
down the Lagrangian equations of motion. Include the constraint forces at
the point of contact and use the coordinate axis indicated on the figure on
the right. (b) What is the value of us at which the disk would begin to slip?
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