Download FA#5--Rotational Dynamics I FA#5

FA#5–Rotational Dynamics 1
AP Physics/MTHS/Matthews
Name: ________________________________________
Directions: Answer the following questions in the space provided. Show any and all necessary work.
(1) A disc (r = 20 cm) has a moment of inertia of 2.0 kgm2. Its angular velocity increases at 4.0 rad/s2.
a. What is the net torque on the disc?
b. What will be the tangential velocity of the outer edge of the disc 6 sec after it starts rotating?
(2) A wheel, which is shaped like a ring (I=1/2mR2), has a mass of 8.2 kg and a diameter of 74 cm. A tangential
force of 50.0 N is applied to the outer edge of the wheel for 5.0 seconds. The wheel is initially at rest.
a. What is the magnitude of the torque being applied to the wheel?
b. What is the moment of inertia of this wheel?
c. What will be the resulting angular acceleration?
(3) What is the average torque needed to accelerate the turbine of a jet engine from rest to a rotational
velocity of 160 rad/s in 25 seconds? The turbine’s rotating parts have a 32 kgm2 rotational inertia.
(4) While sitting in a swivel chair, you push against the floor with your heel to make the chair spin. The 7.0 N
frictional force is applied at a point 40 cm from the chair’s rotation axis, in the direction that causes the
greatest angular acceleration. If that angular acceleration is 1.8 rad/s2, what is the total moment of inertia
about the axis of you and the chair?
(5) The 2.5 kg object shown has a moment of inertia about the rotation axis of
0.085 kgm2. The rotation axis is horizontal. When released, what will be the
object’s initial angular acceleration?
(6) Because of the force M applied by the triceps muscle, a human forearm
can rotate about an axis at the elbow joint to throw a dart. Assume a
forearm has a moment of inertia of 0.065 kgm2, that M acts perpendicular to
the forearm, and ignore gravity, friction or any other forces acting. Calculate
the force M needed to give the dart a tangential speed of 5.0 m/s in 0.1
seconds, starting from rest.
(7) A frictionless pulley, which can be modeled as a 0.9 kg solid cylinder (I = ½
mR2) with a 0.3 m radius, has a rope going over it. The tension in the rope is 10
N on one side and 12 N on the other.
(a) What is the angular acceleration of the pulley?
(b) What is the tangential acceleration of the pulley?
(8) A 9.75-m ladder with a mass of 23.2 kg lies flat on the ground. A painter grabs the top end of the ladder
and pulls straight upward with a force of 245 N. At the instant the top of the ladder leaves the ground, the
ladder experiences an angular acceleration of 1.80 rad/s2 about an axis passing through the bottom end of the
ladder. The ladder's center of gravity lies halfway between the top and bottom ends.
a. What is the net torque acting on the ladder?
b. What is the ladder’s moment of inertia?