Advanced Kinematics and Dynamics MCQs

Q#1: What is the term for the motion of an object around a fixed axis?
(A) Linear motion
(B) Rotational motion
(C) Translational motion
(D) Vibrational motion
Answer: (B) Rotational motion

Q#2: In rotational kinematics, angular displacement is measured in:
(A) Meters
(B) Radians
(C) Seconds
(D) Meters per second
Answer: (B) Radians

Q#3: What is the angular velocity of an object rotating through 6 radians in 2 seconds?
(A) 3 rad/s
(B) 12 rad/s
(C) 1.5 rad/s
(D) 6 rad/s
Answer: (A) 3 rad/s

Q#4: The relationship between linear velocity $v$ and angular velocity $omega$ is:
(A) $v = omega r$
(B) $v = frac{r}{omega}$
(C) $v = frac{omega}{r}$
(D) $v = r/omega$
Answer: (A) $v = omega r$

Q#5: The moment of inertia of a solid sphere about its diameter is:
(A) $frac{1}{2}mr^2$
(B) $frac{2}{5}mr^2$
(C) $frac{2}{3}mr^2$
(D) $frac{1}{3}mr^2$
Answer: (B) $frac{2}{5}mr^2$

Q#6: The equation $F = ma$ represents:
(A) Newton’s First Law
(B) Newton’s Second Law
(C) Newton’s Third Law
(D) Law of Gravitation
Answer: (B) Newton’s Second Law

Q#7: Conservation of angular momentum states that:
(A) Total angular momentum remains constant if no external torque acts
(B) Angular momentum is always zero
(C) Torques must be zero in all systems
(D) External forces conserve momentum
Answer: (A)

Q#8: The centripetal force is given by:
(A) $F = frac{mv^2}{r}$
(B) $F = mr v^2$
(C) $F = frac{mv}{r}$
(D) $F = mromega^2$
Answer: (A)

Q#9: Angular acceleration is the rate of change of:
(A) Angular displacement
(B) Angular velocity
(C) Linear velocity
(D) Torque
Answer: (B) Angular velocity

Q#10: The SI unit of torque is:
(A) Joule
(B) Newton–meter
(C) Watt
(D) Newton
Answer: (B) Newton–meter

Q#11: Work done by a torque through angular displacement $theta$ is:
(A) $W = tau theta$
(B) $W = frac{1}{2}tautheta$
(C) $W = frac{tau}{theta}$
(D) $W = tau/theta$
Answer: (A)

Q#12: Conservation of energy means:
(A) Energy can neither be created nor destroyed
(B) Energy is always kinetic
(C) Energy exists only in closed systems
(D) Energy is lost with friction
Answer: (A)

Q#13: Linear momentum is defined as:
(A) $p = mv$
(B) $p = frac{m}{v}$
(C) $p = v/m$
(D) $p = m/v$
Answer: (A)

Q#14: Impulse equals:
(A) Force × time
(B) Mass × acceleration
(C) Velocity × time
(D) Force × distance
Answer: (A)

Q#15: The work–energy theorem states:
(A) Work done equals change in kinetic energy
(B) Energy is always conserved
(C) Potential energy equals work
(D) Energy equals force
Answer: (A)

Q#16: Rotational form of Newton’s second law is:
(A) $tau = Ialpha$
(B) $tau = ma$
(C) $tau = alpha/I$
(D) $tau = vr$
Answer: (A)

Q#17: Rotational kinetic energy is:
(A) $frac{1}{2}Iomega^2$
(B) $frac{1}{2}mv^2$
(C) $Ialpha^2$
(D) $mr^2omega$
Answer: (A)

Q#18: Motion of a double pendulum is:
(A) Simple harmonic
(B) Chaotic
(C) Linear
(D) Uniform
Answer: (B) Chaotic

Q#19: Coriolis force is given by:
(A) $F = 2m(vec{v} times vec{omega})$
(B) $F = mvomega$
(C) $F = frac{1}{2}mvomega$
(D) $F = momega^2$
Answer: (A)

Q#20: Euler’s equations describe:
(A) Translation
(B) Oscillation
(C) Rigid body rotation
(D) Linear motion
Answer: (C)

Q#21: Centripetal acceleration is:
(A) $a = frac{v^2}{r}$
(B) $a = vr$
(C) $a = omega r$
(D) $a = v/r$
Answer: (A)

Q#22: Gyroscopic effect refers to:
(A) Resistance to change in orientation
(B) Increase in angular velocity
(C) Linear acceleration
(D) Centripetal force
Answer: (A)

Q#23: Fictitious forces arise in a rotating frame due to:
(A) Inertia
(B) Gravity
(C) Acceleration
(D) Rotation
Answer: (D)

Q#24: Lagrangian mechanics is based on:
(A) Force
(B) Energy
(C) Torque
(D) Momentum
Answer: (B)

Q#25: Principle of least action states that:
(A) Action is minimized
(B) Energy is conserved
(C) Force is zero
(D) Work is maximum
Answer: (A)

Q#26: Angular momentum of a particle in circular motion is:
(A) $L = mvr$
(B) $L = mv^2r$
(C) $L = mr^2$
(D) $L = momega r$
Answer: (A)

Q#27: Torque causes:
(A) Angular acceleration
(B) Linear acceleration
(C) Velocity
(D) Inertia change
Answer: (A)

Q#28: Radius of gyration represents:
(A) Equivalent distance where mass is concentrated
(B) Lever arm length
(C) Circular path radius
(D) Distance to center of mass
Answer: (A)

Q#29: Moment of inertia of a solid cylinder about its axis is:
(A) $frac{1}{2}mr^2$
(B) $frac{1}{4}mr^2$
(C) $frac{1}{3}mr^2$
(D) $mr^2$
Answer: (A)

Q#30: Friction in rotational motion:
(A) Decreases angular velocity
(B) Increases angular acceleration
(C) Increases inertia
(D) Stops torque
Answer: (A)