Dynamics Flashcards

A disk has mass 10 kg and radius 0.5 m. What is its mass moment of inertia about its central axis?

Answer: 1.25 kg·m²

I = ½mr² = ½ × 10 × 0.25 = 1.25 kg·m² for a solid disk.

What does the work-energy theorem state for a particle?

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.

A 1500 kg car traveling at 30 m/s brakes to a stop over 60 m. What is the average braking force?

Answer: 11,250 N

Using work-energy: F = ΔKE/d = (½×1500×900)/60 = 675000/60 = 11,250 N.

In a central-force problem, which quantity is conserved along the orbit?

Answer: Angular momentum

For a central force, the torque about the center is zero, so angular momentum is conserved.

The parallel-axis theorem relates the moment of inertia about an axis through the centroid (Ī) to a parallel axis at distance d as:

Answer: I = Ī + md²

The parallel-axis theorem is I = Ī + md², where m is mass and d is the distance between axes.

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?

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).

A rigid body in plane motion has both translation of its center of mass and rotation. The governing equations are:

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.