A string is wrapped around a solid cylinder of mass M and radius R and pulls hor

Question

A string is wrapped around a solid cylinder of mass M and radius R and pulls horizontally with force T from the top of the cylinder. The horizontal surface on which the cylinder rests is frictionless.
a. What is the acceleration of the center of mass of the cylinder?
b. What is the angular acceleration of the cylinder about its center of mass?
c. What is the acceleration (magnitude and direction) of the point on the cylinder which touches the horizontal surface?Make sure your answer is dimensionally correct. Now were going to change the problem and give the surface on which the cylinder rests a nonzero coefficient of static friction, Us.
d. Assuming that the cylinder now rolls without slipping, what is the acceleration of its center of mass?
e. For a given coefficient of static friction, Us, what is the largest acceleration of the center of mass which can be achieved without the cylinder slipping against the surface?

Explanation / Answer

Here ,
a)

Using second law of motion

a = T/M

b)

as there is no friction

angular acceleration = 0

c)
for the bottom point .

a = F/M in the direction of motion

d)

let the acceleration of the com is a

Using second law of motion

a = total force/effective mass

a = T/(M + I/r^2)

a = T/(M + 0.5 * M*r^2/r^2)

a = T/(1.5 M)

a = 0.667 * T/M

the acceleration of centre of mass is 0.667 T/M

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