3 . A ladder of length L leans against a wall at an angle of θ from the horizontal, as shown above. The
normal force FN applied from the ground on the ladder applies what torque about the ladder’s center of
mass?
(A) FN ·(L /2)
(B) FN ·L cos θ
(C) FN ·L sin θ
(D) FN ·(L /2) cos θ
(E) FN ·(L /2) sin θ
4 . The front wheel on an ancient bicycle has a radius of 0.5 m. It moves with angular velocity given by
the function ω (t ) = 2 + 4t 2 , where t is in seconds. About how far does the bicycle move between t =
2 and t = 3 seconds?
(A) 36 m
(B) 27 m
(C) 21 m
(D) 14 m
(E) 7 m
Free Response:
5 . A stick of mass M and length L is pivoted at one end. A small mass m << M is attached to the right-
hand end of the stick. The stick is held horizontally and released from rest.
(a) Given that the rotational inertia of a uniform rod pivoted around one end is (1/3)ML 2 , determine
the rotational inertia of the described contraption.
(b) Calculate the angular velocity of the contraption when it reaches a vertical position.
(c) Calculate the linear velocity of the small mass m when it is at its lowest position.
