Rotational Motion

Angular momentum

________ is conserved in a closed system; that is, when no external torques act on the objects in the system.

Torque

________ occurs when a force is applied to an object, and that force can cause the object to rotate.

lever arm

The "________ "for a force is the closest distance from the fulcrum to the line of that force.

Rotational inertia

________ depends less on the mass of an object than on how that mass is distributed.

massive objects

Tendency for ________ to resist changes in their velocity is referred to as inertia.

Angular momentum

________ is conserved anytime no external torque acts on a system of objects.

rotational inertia

The ________, I, is the rotational equivalent of mass.

Angular momentum

________ is the amount of effort it would take to make a rotating object stop spinning.

All of the objects mentioned in the choices below have the same total mass and length. Which has the greatest rotational inertia about its midpoint?

(A) a very light rod with heavy balls attached at either end

(B) a uniform rod

(C) a nonuniform rod, with the linear density increasing from one end to the other

(D) a nonuniform rod, with the linear density increasing from the middle to the ends

(E) a very light rod with heavy balls attached near the midpoint

A—The farther the mass from the midpoint, the larger its contribution to the rotational inertia. In choice A the mass is as far as possible from the midpoint; because all items have the same mass, A must have the largest I.

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

D—The angular position function is given by the integral of the angular velocity function with respect to time. The limits on the integral are 2 and 3 seconds: this evaluates to approximately 27 radians. Using x = rθ, the distance traveled is closest to 14 m.

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.

Given that the rotational inertia of a uniform rod pivoted around one end is (1/3)ML2 , determine the rotational inertia of the described contraption

The rotational inertia of the entire contraption is the sum of the moments of inertia for each part. I for the rod is given; I for a point mass a distance L from the pivot is mL2 . So, I total = (1/3)ML2 + mL2 . Be sure to differentiate between M and m.