1. A 45-kg girl is sitting on a seesaw 0.6 m from the balance point, as shown below. How far, on the other side, should a 60-kg boy sit so that the seesaw will remain in balance?

2. A balanced stick is shown below. The distance from the fulcrum is shown for each mass except the 10-g mass. What is the approximate position of the 10-g mass, based on the diagram?

3. A solid cylinder consisting of an outer radius r₁ and an inner radius r₂ is pivoted on a frictionless axle as shown below. A string is wound around the outer radius and is pulled to the right with a force F₁ = 3 N. A second string is wound around the inner radius and is pulled down with a force F₂ = 5 N. If r₁ = 0.75 m and r₂ = 0.35 m, what is the net torque acting on the cylinder?

Answer questions 4 and 5 based on the following diagram. The rod is considered massless.

4. What is the net torque about an axis through point A?

(A) 16.8 N · m
(B) 15.2 N · m
(C) −5.5 N · m
(D) −7.8 N · m

5. What is the net torque about an axis through point C?

(A) 3.5 N · m
(B) 7.5 N · m
(C) −15.2 N · m
(D) 5.9 N · m

6. Compute the average angular acceleration and the angular displacement during the 2 seconds a rotating object speeds up from 0.5 rad/s to 0.7 rad/s.

(A) α = 0.1 rad/s²       Δθ = 0.3 radians
(B) α = 0.2 rad/s²       Δθ = 0.5 radians
(C) α = 0.1 rad/s²       Δθ = 1.2 radians
(D) α = 0.2 rad/s²       Δθ = 1.2 radians

7. An object with a moment of inertia I experiences a net torque of T. If the object is initially at rest, what is its angular speed after 3 seconds of this torque?

(A) 3I T
(B) 9I T
(C) 3I/T
(D) 3T/I

8. If a spinning ball of clay on top of a freely turning frictionless tabletop increases its rotational inertia by 50 percent by bulging outward, what will happen to the rotational speed of the clay and tabletop?

(A) It will be half as fast.
(B) It will be 1.5 times faster.
(C) It will be 4 times slower.
(D) It will be slower by a factor of 2/3.

1. A 500-N person stands 2.5 m from a wall against which a horizontal beam is attached. The beam is 6 m long and weighs 200 N (see diagram below). A cable attached to the free end of the beam makes an angle of 45° to the horizontal and is attached to the wall.

2. A uniform ladder of length ℓ and weight 100 N rests against a smooth vertical wall. The coefficient of static friction between the bottom of the ladder and the floor is 0.5.

3. A rotating toy top (moment of inertia = 0.012 kg m²) is rotating 8 times per second while encountering a friction torque of 0.2 Nm. For how much more time will it be rotating?