Download class work 7: planar kinetics of a rigid body force and acceleration

CLASS WORK 7: PLANAR KINETICS OF A RIGID BODY
FORCE AND ACCELERATION
April 14, 2017
3. The pendulum consists of two thin rods, each having a weight of
10 lb and suspended from point O as shown in the figure below.
Compute the pendulum’s moment of inertia about an axis passing through (a) the pin at O, and (b) the mass center G of the
pendulum.
1. Determine the moment of inertia of the cylinder shown in the figure
below about the z-axis. The density ρ of the material is constant
2. A solid is formed by revolving the shaded area shown in the figure
below about the y-axis. If the density of the material is 5 slug/f t3 ,
determine the moment of inertia about the y-axis
4. The 100 kg beam BD shown in the figure below is supported by
two rods having negligible mass. Determine the force created in
each rod if at the instant θ = 30o the rods are both rotating with
an angular velocity of ω = 6 rad/s.
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5. The 20 kg slender rod shown in the figure below is rotating in the
vertical plane, and at the instant shown it has an angular velocity
of ω = 5 rad/s. Determine the rod’s angular acceleration and the
horizontal and vertical components of reaction at the pin at this
instant.
8. A uniform slender pole shown in the figure below has a mass of
100 kg and a moment of inertia IG = 75 kg · m2 . If the coefficients
of static and kinetic friction between the end of the pole and the
surface are µs = 0.3 and µk = 0.25, respectively, determine the
pole’s angular acceleration at the instant the 400 N horizontal
force is applied. The pole is originally at rest.
6. The unbalanced 50 lb flywheel shown in the figure below has a
radius of gyration of kG = 0.6 f t about an axis passing through its
mass center. If it has clockwise angular velocity of 8 ras/s at the
instant shown, determine the horizontal and vertical components
of reaction at the pin.
7. The 50 lb wheel shown in the figure below has a radius of gyration
kG = 0.7 f t. If a 35 lb · f t couple moment is applied to the wheel,
determine the acceleration of its mass center G. The coefficients of
static and kinetic friction between the wheel and the plane at A
are µs = 0.3 and µk = 0.25 respectively.
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