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 = 0.6 mn = 1800 rpm130 kg

A flywheel is a uniform solid disc of mass 130 kg and radius 0.6 m. It spins at 1800 rpm. Find its kinetic energy Ek in kJ.

M = 130 kgR = 0.6 mn = 1800 rpm
Ek = kJ
2.Easy
k = 0.25 mn = 2600 rpm210 kg

A flywheel of mass 210 kg has a radius of gyration of 0.25 m about its axis. It spins at 2600 rpm. Find its kinetic energy Ek in kJ.

M = 210 kgk = 0.25 mn = 2600 rpm
Ek = kJ
3.Medium
ω = ?L = 1 mm = 6.5 kg

A uniform slender rod of mass 6.5 kg and length 1 m is pinned at one end and released from rest in a horizontal position. Ignore friction and use g = 9.81 m/s². Find the angular velocity ω of the rod as it swings through the vertical position.

m = 6.5 kgL = 1 mg = 9.81 m/s²
ω = rad/s
4.Medium
13.5 kgaαM = 14.5 kgR = 0.2 m

A 13.5 kg block hangs from a light cord wrapped around a pulley, a uniform solid disc of mass 14.5 kg and radius 0.2 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 = 13.5 kgM = 14.5 kgR = 0.2 mg = 9.81 m/s²
T = N
5.Hard
0.7 m0.15 mn1​ = 20 rpm

A person stands on a frictionless turntable and holds a 6 kg dumbbell in each hand, 0.7 m from the axis. The person and turntable alone have a moment of inertia of 1.5 kg·m² about the axis. They turn at 20 rpm, then pull the dumbbells in to 0.15 m from the axis. Treat the dumbbells as point masses. Find the new speed n2 in rpm.

I0 = 1.5 kg·m²m = 2 × 6 kgr1 = 0.7 mr2 = 0.15 mn1 = 20 rpm
n2 = rpm
6.Hard
θ = 20°as = 5.5 m

A thin hoop rolls without slipping down a slope inclined at 20° to the horizontal. Use g = 9.81 m/s². It starts from rest. How long t does it take to roll 5.5 m down the slope?

θ = 20°I = m·r²g = 9.81 m/s²s = 5.5 m
t = s

Answer key

  1. 1. Ek = 415.7 kJ
  2. 2. Ek = 486.5 kJ
  3. 3. ω = 5.425 rad/s
  4. 4. T = 46.27 N
  5. 5. n2 = 83.39 rpm
  6. 6. t = 2.561 s

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