A uniform circular motion can be considered as a combination of ______.

A uniform circular motion can be considered as a combination of ______.

• A. Linear velocity and impulse
• B. Simple harmonic motion and momentum
• C. Rectilinear translation and curvilinear translation
• D. Two simple harmonic motions

Answer: (D)

Uniform circular motion can be understood as the result of two independent simple harmonic motions along perpendicular directions with the same frequency. If you describe the position of the particle as x(t) = R cos(ωt) and y(t) = R sin(ωt), each coordinate undergoes simple harmonic motion with amplitude R and angular frequency ω. The two SHMs are 90 degrees out of phase, and together they trace a circle when combined. This perspective explains why the motion is described as a sum of two SHMs: each axis contributes an SHM, and their equal amplitude and phase relationship produce the circular path. The other descriptions don’t capture this natural decomposition into perpendicular SHMs that yields the circular trajectory.

Uniform circular motion can be understood as the result of two independent simple harmonic motions along perpendicular directions with the same frequency. If you describe the position of the particle as x(t) = R cos(ωt) and y(t) = R sin(ωt), each coordinate undergoes simple harmonic motion with amplitude R and angular frequency ω. The two SHMs are 90 degrees out of phase, and together they trace a circle when combined. This perspective explains why the motion is described as a sum of two SHMs: each axis contributes an SHM, and their equal amplitude and phase relationship produce the circular path. The other descriptions don’t capture this natural decomposition into perpendicular SHMs that yields the circular trajectory.