NCEES Dynamics 4 — Questions and Answers
Question 1: A disk has mass 10 kg and radius 0.5 m. What is its mass moment of inertia about its central axis?
- 1.25 kg·m² (Correct answer)
- 2.5 kg·m²
- 5.0 kg·m²
- 0.625 kg·m²
Correct answer: 1.25 kg·m²
I = ½mr² = ½ × 10 × 0.25 = 1.25 kg·m² for a solid disk.
Question 2: What does the work-energy theorem state for a particle?
- Net work equals the change in kinetic energy (Correct answer)
- Net work equals the change in potential energy
- Net work equals the total mechanical energy
- Net work equals impulse
Correct answer: Net work equals the change in kinetic energy
The work-energy theorem states that the net work done on a particle equals its change in kinetic energy.
Question 3: A 1500 kg car traveling at 30 m/s brakes to a stop over 60 m. What is the average braking force?
- 11,250 N (Correct answer)
- 22,500 N
- 750 N
- 5,625 N
Correct answer: 11,250 N
Using work-energy: F = ΔKE/d = (½×1500×900)/60 = 675000/60 = 11,250 N.
Question 4: In a central-force problem, which quantity is conserved along the orbit?
- Angular momentum (Correct answer)
- Linear momentum
- Kinetic energy only
- Potential energy only
Correct answer: Angular momentum
For a central force, the torque about the center is zero, so angular momentum is conserved.
Question 5: The parallel-axis theorem relates the moment of inertia about an axis through the centroid (Ī) to a parallel axis at distance d as:
- I = Ī + md² (Correct answer)
- I = Ī − md²
- I = Ī × d²
- I = Ī / d²
Correct answer: I = Ī + md²
The parallel-axis theorem is I = Ī + md², where m is mass and d is the distance between axes.
Question 6: A 0.5 kg ball hits a wall at 10 m/s and rebounds at 8 m/s. What is the impulse exerted by the wall on the ball?
- 9 N·s toward ball (Correct answer)
- 1 N·s away from wall
- 9 N·s away from wall
- 5 N·s toward ball
Correct answer: 9 N·s toward ball
Impulse = Δp = m(v_f − v_i) = 0.5(8−(−10)) = 0.5×18 = 9 N·s directed toward the ball (away from wall).
Question 7: A rigid body in plane motion has both translation of its center of mass and rotation. The governing equations are:
- ΣF = m·a_G and ΣM_G = I_G·α (Correct answer)
- ΣF = I·α and ΣM = m·a
- ΣF = m·v and ΣM = I·ω
- ΣF = ½mv² and ΣM = ½Iω²
Correct answer: ΣF = m·a_G and ΣM_G = I_G·α
For general plane motion, Newton's law gives ΣF = m·a_G for translation and ΣM_G = I_G·α for rotation.
NCEES Dynamics 4
A disk has mass 10 kg and radius 0.5 m.
What is its mass moment of inertia about its central axis?