Question

A small, solid cylinder with mass = 20 kg and radius = 0.10 m starts from rest and rotates without friction about a fixed axis through its center of mass. A string is wrapped around the circumference of the cylinder and pulled using a constant force F. The resulting angular acceleration of the cylinder is 5.0 rad/s2. What's the angular velocity after 4.0 s, in radians per second? (The moment of inertia of the cylinder is 1 half M R squared.)

QUESTION 9 A small, solid cylinder with mass = 20 kg and radius = 0.10 m starts from rest and rotates without friction about a fixed axis through its center of mass. A string is wrapped around the circumference of the cylinder and pulled using a constant force F. The resulting angular acceleration of the cylinder is 5.0 rad/s2. What length of string has unwound after 4.0 s, in meters? (The moment of inertia of the cylinder is 1 half M R squared.)

Answer 1

Solution:

1.)

Using angular kinematics,

= t

= 5*4

= 20 rad/s

2.)

Using angular kinematics,

= 1/2t²

= 0.5*5*4²

= 40 rad.

Length unwound is l = r = 40*0.1 = 4 m.

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