NCEES Dynamics 5

Question 1

A 2 kg mass on a spring (k = 200 N/m) undergoes simple harmonic motion. What is its natural frequency ωn?

Accepted Answer

10 rad/s

Answer

ωn = √(k/m) = √(200/2) = √100 = 10 rad/s.

Question 2

A satellite in circular orbit at radius r from the Earth's center has speed v. If r doubles, what happens to v?

Accepted Answer

v decreases by factor √2

Answer

v = √(GM/r); doubling r gives v' = v/√2, a decrease by factor √2.

Question 3

What is the velocity of the center of mass of a system of particles with masses m1=2 kg (v1=3 m/s) and m2=4 kg (v2=−1 m/s)?

Accepted Answer

1/3 m/s

Answer

v_cm = (m1v1 + m2v2)/(m1+m2) = (6−4)/6 = 2/6 = 1/3 m/s.

Question 4

D'Alembert's principle converts a dynamic problem into an equivalent static problem by introducing:

Accepted Answer

An inertia force −ma opposing acceleration

Answer

D'Alembert's principle adds the inertia vector −ma to the free-body diagram, yielding a pseudo-static equilibrium.

Question 5

A gyroscope spinning at high speed has its spin axis horizontal. When a torque is applied vertically, the axis precesses. The precession rate Ω is given by:

Accepted Answer

Ω = M/(I·ω)

Answer

Precession rate Ω = M/(I·ω), where M is the applied torque, I is moment of inertia, and ω is spin rate.

NCEES Practice Test

NCEES Practice Test

NCEES Dynamics 5