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 = 0.4 mn = 600 rpm40 kg

A flywheel of mass 40 kg has a radius of gyration of 0.4 m about its axis. It spins at 600 rpm. Find its kinetic energy Ek in kJ.

M = 40 kgk = 0.4 mn = 600 rpm
Ek = kJ
2.Easy
R = 0.2 mn = 800 rpm180 kg

A flywheel is a uniform solid disc of mass 180 kg and radius 0.2 m. It spins at 800 rpm. Find its kinetic energy Ek in kJ.

M = 180 kgR = 0.2 mn = 800 rpm
Ek = kJ
3.Medium
n = 600 rpmTb​ = 170 N·mI = 34 kg·m²

A flywheel with a moment of inertia of 34 kg·m² spins at 600 rpm. A brake applies a constant friction torque of 170 N·m. How long t does it take to stop?

I = 34 kg·m²n = 600 rpmTb = 170 N·m
t = s
4.Medium
6.5 kgaαM = 17 kgR = 0.15 m

A 6.5 kg block hangs from a light cord wrapped around a pulley, a uniform solid disc of mass 17 kg and radius 0.15 m that turns on a frictionless horizontal axle. The block is released from rest. Use g = 9.81 m/s². Find the tension T in the cord.

m = 6.5 kgM = 17 kgR = 0.15 mg = 9.81 m/s²
T = N
5.Hard
θ = 40°as = 3 m

A thin hoop rolls without slipping down a slope inclined at 40° to the horizontal. Use g = 9.81 m/s². It starts from rest. How long t does it take to roll 3 m down the slope?

θ = 40°I = m·r²g = 9.81 m/s²s = 3 m
t = s
6.Hard
580 m/s10 g0.5 mL = 1 m4 kgφ

A uniform slender rod of mass 4 kg and length 1 m hangs at rest from a frictionless pivot at its top end. A 10 g bullet moving horizontally at 580 m/s hits the rod 0.5 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 = 4 kgL = 1 mm = 10 gv = 580 m/sd = 0.5 mg = 9.81 m/s²
φ = °

Answer key

  1. 1. Ek = 12.63 kJ
  2. 2. Ek = 12.63 kJ
  3. 3. t = 12.57 s
  4. 4. T = 36.13 N
  5. 5. t = 1.38 s
  6. 6. φ = 32.86 °

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