Variable Angular Acceleration & Non-Uniform Motion — IISER Physics MCQs with Solutions
Free IISER Physics Variable Angular Acceleration & Non-Uniform Motion MCQs with step-by-step solutions (8 questions). Part of Circular Motion. Practise online on Prepizo — no login needed.
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Questions with solutions
Q1 — Variable Angular Acceleration & Non-Uniform Motion · easy · theory
In NON-uniform circular motion, the net acceleration is:
A. Zero
B. Purely tangential
C. Purely radial
D. Neither purely radial nor purely tangential — it has both components ✓ Correct
Solution: Speed changes (a_t ≠ 0) while direction changes (a_c ≠ 0): the total acceleration tilts away from the radius.
Q2 — Variable Angular Acceleration & Non-Uniform Motion · medium · theory
The angular kinematics equations (ω = ω₀ + αt, etc.) may be used only when:
A. The motion is circular
B. ω is small
C. The angular acceleration α is constant ✓ Correct
D. The radius is constant
Solution: They are the rotational analogues of constant-acceleration kinematics; for α(t) or α(θ) you must integrate.
Q3 — Variable Angular Acceleration & Non-Uniform Motion · easy · numerical
A wheel's angular speed grows as ω = 4t (rad/s). Its angular acceleration and the angle swept in 2 s are:
A. 4 rad/s² and 8 rad ✓ Correct
B. 4 rad/s² and 16 rad
C. 2 rad/s² and 4 rad
D. 8 rad/s² and 8 rad
Solution: α = dω/dt = 4 rad/s²; θ = ∫ω dt = 2t² = 8 rad at t = 2 s.
Q4 — Variable Angular Acceleration & Non-Uniform Motion · medium · numerical
A flywheel has α = 6t (rad/s²) and starts from rest. Its angular speed at t = 2 s is:
A. 24 rad/s
B. 3 rad/s
C. 12 rad/s ✓ Correct
D. 6 rad/s
Solution: ω = ∫6t dt = 3t² = 12 rad/s. Trap: NOT ω = αt (α is not constant).
Q5 — Variable Angular Acceleration & Non-Uniform Motion · hard · numerical
A particle's angular acceleration depends on angle as α = 4θ (rad/s²), starting from rest at θ = 0. Its angular speed at θ = 2 rad is:
A. 8 rad/s
B. 2√2 rad/s
C. 4 rad/s ✓ Correct
D. 16 rad/s
Solution: ω dω = α dθ ⇒ ω²/2 = ∫₀² 4θ dθ = 8 ⇒ ω = 4 rad/s.
Q6 — Variable Angular Acceleration & Non-Uniform Motion · medium · numerical
A fan slows uniformly from 30 rad/s to rest in 15 s. The total angle turned during the stop is:
A. 30 rad
B. 112.5 rad
C. 450 rad
D. 225 rad ✓ Correct
Solution: θ = (ω₀ + 0)/2 × t = 15×15 = 225 rad.
Q7 — Variable Angular Acceleration & Non-Uniform Motion · hard · theory
A particle moves on a circle so that its speed is proportional to time (v = kt). The ratio of the magnitudes of its tangential and centripetal accelerations:
A. Decreases as 1/t² — a_c eventually dominates ✓ Correct
B. Grows with t
C. Equals 1 always
D. Stays constant
Solution: a_t = k (constant); a_c = v²/r = k²t²/r grows as t². a_t/a_c = r/(kt²) → 0: the motion becomes acceleration-dominated radially.
Q8 — Variable Angular Acceleration & Non-Uniform Motion · hard · numerical
A particle starts from rest on a circle of radius 1 m with constant tangential acceleration a_t = 2 m/s². The time at which the centripetal acceleration equals the tangential acceleration is:
A. 1/√2 ≈ 0.71 s ✓ Correct
B. 2 s
C. √2 s
D. 1 s
Solution: v = 2t ⇒ a_c = v²/r = 4t². Setting 4t² = 2 gives t² = 1/2 ⇒ t = 1/√2 ≈ 0.71 s.