A cylinder of radius R, length L, and mass M is released from rest on a slope inclined at angle θ. It is oriented to roll straight down the slope. If the slope were frictionless, the cylinder would slide down the slope without rotating. What minimum coefficient of static
friction is needed for the cylinder to roll down without slipping?
Coefficient of friction is
A cylinder of radius= R,
length = L, and
mass = M is released from rest on a slope
angle of inclination= θ
Lets first draw the free body diagram as below
Equate horizontal and vertical force
As net force in perpendicular direction is zero so
N = mg cosθ ............................(1)
mg sinθ - fs = ma ........................(2)
Where fs is frictional force
Find the torque acting on cylinder.
As mass passes through axis of center so only frictional force will cause the torque
Torque is also expressed as
Now substitute the value of fs in equation (1)
We know frictional force is
Substitute the value from equation(1) and (3)
A 75 g, 30-cm-long rod hangs vertically on a frictionless, horizontal axle passing through its center. A 10 g ball of clay traveling horizontally at 2.5 m/s hits and sticks to the very
bottom tip of the rod. To what maximum angle, measured from vertical, does the rod (with the attached ball of clay) rotate?
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