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
R = 0.25 mn = 800 rpm220 kg

A flywheel is a uniform solid disc of mass 220 kg and radius 0.25 m. It spins at 800 rpm. Find its kinetic energy Ek in kJ.

M = 220 kgR = 0.25 mn = 800 rpm
Ek = kJ
2.Easy
R = 0.25 mn = 2900 rpm280 kg

A flywheel is a uniform solid disc of mass 280 kg and radius 0.25 m. It spins at 2900 rpm. Find its kinetic energy Ek in kJ.

M = 280 kgR = 0.25 mn = 2900 rpm
Ek = kJ
3.Medium
L = 2.7 mm = 19 kgα

A uniform slender rod of mass 19 kg and length 2.7 m is pinned at one end and held horizontal. It is released from rest. Use g = 9.81 m/s². Find the acceleration atip of the free end just after release.

m = 19 kgL = 2.7 mg = 9.81 m/s²
atip = m/s²
4.Medium
v = ?3.5 kgL = 1.1 mm = 3 kg

A uniform slender rod of mass 3 kg and length 1.1 m is pinned at one end and released from rest in a horizontal position. A small ball of mass 3.5 kg is fixed to its free end. Ignore friction and use g = 9.81 m/s². Find the speed v of the free end as the rod swings through the vertical position.

m = 3 kgL = 1.1 mmball = 3.5 kgg = 9.81 m/s²
v = m/s
5.Hard
θ = 25°as = 9 m

A thin hoop rolls without slipping down a slope inclined at 25° to the horizontal. Use g = 9.81 m/s². It starts from rest. How long t does it take to roll 9 m down the slope?

θ = 25°I = m·r²g = 9.81 m/s²s = 9 m
t = s
6.Hard
520 m/s35 g0.49 mL = 0.6 m1.5 kg

A uniform slender rod of mass 1.5 kg and length 0.6 m hangs at rest from a frictionless pivot at its top end. A 35 g bullet moving horizontally at 520 m/s hits the rod 0.49 m below the pivot and stays embedded. Find the angular velocity ω of the rod just after the impact.

M = 1.5 kgL = 0.6 mm = 35 gv = 520 m/sd = 0.49 m
ω = rad/s

Answer key

  1. 1. Ek = 24.13 kJ
  2. 2. Ek = 403.5 kJ
  3. 3. atip = 14.71 m/s²
  4. 4. v = 4.897 m/s
  5. 5. t = 2.947 s
  6. 6. ω = 47.33 rad/s

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