Rigid-body rotation worksheet with answers

Free printable Rigid-body rotation worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

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1.Easy
k = 0.55 mn = 1600 rpm90 kg

A flywheel of mass 90 kg has a radius of gyration of 0.55 m about its axis. It spins at 1600 rpm. Find its kinetic energy Ek in kJ.

M = 90 kgk = 0.55 mn = 1600 rpm
Ek = kJ
2.Easy
k = 0.4 m0 → 1800 rpm80 kg

A flywheel of mass 80 kg with a radius of gyration of 0.4 m is accelerated uniformly from rest to 1800 rpm. This takes 17 s. Ignoring friction, find the constant torque T needed.

m = 80 kgk = 0.4 mn1 = 0 rpmn2 = 1800 rpmt = 17 s
T = N·m
3.Medium
3.5 kgaαM = 4.5 kgR = 0.5 m

A 3.5 kg block hangs from a light cord wrapped around a pulley, a uniform solid disc of mass 4.5 kg and radius 0.5 m that turns on a frictionless horizontal axle. The block is released from rest. Use g = 9.81 m/s². Find the acceleration a of the block.

m = 3.5 kgM = 4.5 kgR = 0.5 mg = 9.81 m/s²
a = m/s²
4.Medium
n = 1100 rpmTb​ = 120 N·mI = 13.5 kg·m²

A flywheel with a moment of inertia of 13.5 kg·m² spins at 1100 rpm. A brake applies a constant friction torque of 120 N·m. How long t does it take to stop?

I = 13.5 kg·m²n = 1100 rpmTb = 120 N·m
t = s
5.Hard
0.65 m0.25 mn1​ = 55 rpm

A person stands on a frictionless turntable and holds a 2 kg dumbbell in each hand, 0.65 m from the axis. The person and turntable alone have a moment of inertia of 2 kg·m² about the axis. They turn at 55 rpm, then pull the dumbbells in to 0.25 m from the axis. Treat the dumbbells as point masses. Find the new speed n2 in rpm.

I0 = 2 kg·m²m = 2 × 2 kgr1 = 0.65 mr2 = 0.25 mn1 = 55 rpm
n2 = rpm
6.Hard
520 m/s30 g0.57 mL = 1.3 m7.5 kgφ

A uniform slender rod of mass 7.5 kg and length 1.3 m hangs at rest from a frictionless pivot at its top end. A 30 g bullet moving horizontally at 520 m/s hits the rod 0.57 m below the pivot and stays embedded. Use g = 9.81 m/s². Find the largest angle φ from the vertical through which the rod swings.

M = 7.5 kgL = 1.3 mm = 30 gv = 520 m/sd = 0.57 mg = 9.81 m/s²
φ = °

Answer key

  1. 1. Ek = 382.2 kJ
  2. 2. T = 141.9 N·m
  3. 3. a = 5.971 m/s²
  4. 4. t = 12.96 s
  5. 5. n2 = 90.2 rpm
  6. 6. φ = 36.34 °

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