Dynamics 2 Exam 4 – Engineering Mechanics
Practice Questions, Answers & Comprehensive
Exam Review 2026/2027
SECTION I — RIGID-BODY KINEMATICS: TRANSLATION & ROTATION ABOUT A
FIXED AXIS
1. A rigid body rotates about a fixed axis with constant angular acceleration α = 4
rad/s². Starting from rest, what is its angular velocity after 3 s?
A. 6 rad/s
B. 12 rad/s
C. 18 rad/s
D. 24 rad/s
Correct: B. 12 rad/s
ω = ω₀ + αt = 0 + (4)(3) = 12 rad/s. The other options come from
misapplying the kinematic equation (e.g., using ½αt² for velocity or doubling t).
2. For a rigid body in pure translation, which statement is true?
A. All points have the same velocity and acceleration.
B. Angular velocity is nonzero.
C. Points on the body trace circular paths.
D. Velocity varies linearly with distance from the mass center.
Correct: A. All points have the same velocity and acceleration.
In translation, there is no rotation (ω = 0, α = 0), so every point shares
identical velocity and acceleration vectors. Circular paths (C) and linear velocity
variation (D) describe rotation about a fixed axis.
,3. A wheel of radius 0.5 m rotates at 20 rad/s. What is the linear speed of a point
on its rim?
A. 5 m/s
B. 10 m/s
C. 20 m/s
D. 40 m/s
Correct: B. 10 m/s
v = ωr = (20)(0.5) = 10 m/s. Option D incorrectly multiplies by 2r; option A
divides instead of multiplies.
4. SATA — Which quantities are the same for all points on a rigid body rotating
about a fixed axis?
A. Angular velocity ω
B. Angular acceleration α
C. Linear speed v
D. Tangential acceleration aₜ
E. Centripetal acceleration aₙ
Correct: A, B
ω and α are body properties, identical everywhere. Linear speed,
tangential acceleration, and centripetal acceleration all depend on radial distance
r (v = ωr, aₜ = αr, aₙ = ω²r), so they vary point to point.
5. A disk accelerates uniformly from 10 rad/s to 30 rad/s in 5 s. How many
revolutions does it make?
A. ≈ 15.9 rev
B. ≈ 31.8 rev
C. ≈ 100 rev
D. ≈ 6.4 rev
, Correct: A. ≈ 15.9 rev
α = (30−10)/5 = 4 rad/s². θ = ω₀t + ½αt² = (10)(5) + ½(4)(25) = 50 + 50 = 100
rad. 100/(2π) ≈ 15.9 rev. Option C forgets the 2π conversion.
6. A point on a rotating body has tangential acceleration 6 m/s² and centripetal
acceleration 8 m/s². What is the magnitude of total acceleration?
A. 2 m/s²
B. 10 m/s²
C. 14 m/s²
D. 48 m/s²
Correct: B. 10 m/s²
a = √(aₜ² + aₙ²) = √(36 + 64) = √100 = 10 m/s². The components are
perpendicular, so they add vectorially, not arithmetically (C).
7. A pulley of radius 0.2 m has angular acceleration 5 rad/s². What is the
tangential acceleration of a point on its rim?
A. 0.04 m/s²
B. 0.5 m/s²
C. 1.0 m/s²
D. 25 m/s²
Correct: C. 1.0 m/s²
aₜ = αr = (5)(0.2) = 1.0 m/s². Option D mistakenly squares ω-like terms;
option A multiplies r².
8. The number of independent coordinates needed to fully describe a rigid body
in general plane motion is:
A. 1
B. 2
, C. 3
D. 6
Correct: C. 3
General plane motion needs two translation coordinates (x, y) plus one
rotation angle θ = 3 DOF. A 6-DOF body is fully spatial (3 translations + 3
rotations).
9. A fan blade rotates at 300 rpm. What is its angular velocity in rad/s?
A. ≈ 5 rad/s
B. ≈ 31.4 rad/s
C. ≈ 300 rad/s
D. ≈ 50 rad/s
Correct: B. ≈ 31.4 rad/s
ω = 300 × (2π/60) = 300 × 0.1047 ≈ 31.4 rad/s. Option D incorrectly uses
π/60 instead of 2π/60.
10. SATA — For rotation about a fixed axis, which equations are valid when α is
constant?
A. ω = ω₀ + αt
B. θ = ω₀t + ½αt²
C. ω² = ω₀² + 2αθ
D. θ = ωt − ½αt² (with ω = final)
E. v = ωr for rim points
Correct: A, B, C, E
A, B, C are the standard constant-α rotational kinematics equations. E is
the rim-speed relation. D is a miswritten form; the correct alternate is θ = ½(ω₀ +
ω)t.
Practice Questions, Answers & Comprehensive
Exam Review 2026/2027
SECTION I — RIGID-BODY KINEMATICS: TRANSLATION & ROTATION ABOUT A
FIXED AXIS
1. A rigid body rotates about a fixed axis with constant angular acceleration α = 4
rad/s². Starting from rest, what is its angular velocity after 3 s?
A. 6 rad/s
B. 12 rad/s
C. 18 rad/s
D. 24 rad/s
Correct: B. 12 rad/s
ω = ω₀ + αt = 0 + (4)(3) = 12 rad/s. The other options come from
misapplying the kinematic equation (e.g., using ½αt² for velocity or doubling t).
2. For a rigid body in pure translation, which statement is true?
A. All points have the same velocity and acceleration.
B. Angular velocity is nonzero.
C. Points on the body trace circular paths.
D. Velocity varies linearly with distance from the mass center.
Correct: A. All points have the same velocity and acceleration.
In translation, there is no rotation (ω = 0, α = 0), so every point shares
identical velocity and acceleration vectors. Circular paths (C) and linear velocity
variation (D) describe rotation about a fixed axis.
,3. A wheel of radius 0.5 m rotates at 20 rad/s. What is the linear speed of a point
on its rim?
A. 5 m/s
B. 10 m/s
C. 20 m/s
D. 40 m/s
Correct: B. 10 m/s
v = ωr = (20)(0.5) = 10 m/s. Option D incorrectly multiplies by 2r; option A
divides instead of multiplies.
4. SATA — Which quantities are the same for all points on a rigid body rotating
about a fixed axis?
A. Angular velocity ω
B. Angular acceleration α
C. Linear speed v
D. Tangential acceleration aₜ
E. Centripetal acceleration aₙ
Correct: A, B
ω and α are body properties, identical everywhere. Linear speed,
tangential acceleration, and centripetal acceleration all depend on radial distance
r (v = ωr, aₜ = αr, aₙ = ω²r), so they vary point to point.
5. A disk accelerates uniformly from 10 rad/s to 30 rad/s in 5 s. How many
revolutions does it make?
A. ≈ 15.9 rev
B. ≈ 31.8 rev
C. ≈ 100 rev
D. ≈ 6.4 rev
, Correct: A. ≈ 15.9 rev
α = (30−10)/5 = 4 rad/s². θ = ω₀t + ½αt² = (10)(5) + ½(4)(25) = 50 + 50 = 100
rad. 100/(2π) ≈ 15.9 rev. Option C forgets the 2π conversion.
6. A point on a rotating body has tangential acceleration 6 m/s² and centripetal
acceleration 8 m/s². What is the magnitude of total acceleration?
A. 2 m/s²
B. 10 m/s²
C. 14 m/s²
D. 48 m/s²
Correct: B. 10 m/s²
a = √(aₜ² + aₙ²) = √(36 + 64) = √100 = 10 m/s². The components are
perpendicular, so they add vectorially, not arithmetically (C).
7. A pulley of radius 0.2 m has angular acceleration 5 rad/s². What is the
tangential acceleration of a point on its rim?
A. 0.04 m/s²
B. 0.5 m/s²
C. 1.0 m/s²
D. 25 m/s²
Correct: C. 1.0 m/s²
aₜ = αr = (5)(0.2) = 1.0 m/s². Option D mistakenly squares ω-like terms;
option A multiplies r².
8. The number of independent coordinates needed to fully describe a rigid body
in general plane motion is:
A. 1
B. 2
, C. 3
D. 6
Correct: C. 3
General plane motion needs two translation coordinates (x, y) plus one
rotation angle θ = 3 DOF. A 6-DOF body is fully spatial (3 translations + 3
rotations).
9. A fan blade rotates at 300 rpm. What is its angular velocity in rad/s?
A. ≈ 5 rad/s
B. ≈ 31.4 rad/s
C. ≈ 300 rad/s
D. ≈ 50 rad/s
Correct: B. ≈ 31.4 rad/s
ω = 300 × (2π/60) = 300 × 0.1047 ≈ 31.4 rad/s. Option D incorrectly uses
π/60 instead of 2π/60.
10. SATA — For rotation about a fixed axis, which equations are valid when α is
constant?
A. ω = ω₀ + αt
B. θ = ω₀t + ½αt²
C. ω² = ω₀² + 2αθ
D. θ = ωt − ½αt² (with ω = final)
E. v = ωr for rim points
Correct: A, B, C, E
A, B, C are the standard constant-α rotational kinematics equations. E is
the rim-speed relation. D is a miswritten form; the correct alternate is θ = ½(ω₀ +
ω)t.
