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 = 0.5 mn = 1400 rpm100 kg

A flywheel of mass 100 kg has a radius of gyration of 0.5 m about its axis. It spins at 1400 rpm. Find its kinetic energy Ek in kJ.

M = 100 kgk = 0.5 mn = 1400 rpm
Ek = kJ
2.Easy
R = 0.65 mn = 1500 rpm190 kg

A flywheel is a uniform solid disc of mass 190 kg and radius 0.65 m. It spins at 1500 rpm. Find its kinetic energy Ek in kJ.

M = 190 kgR = 0.65 mn = 1500 rpm
Ek = kJ
3.Medium
v = ?2 kgL = 0.9 mm = 1.5 kg

A uniform slender rod of mass 1.5 kg and length 0.9 m is pinned at one end and released from rest in a horizontal position. A small ball of mass 2 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 = 1.5 kgL = 0.9 mmball = 2 kgg = 9.81 m/s²
v = m/s
4.Medium
n = 900 rpmP = 90 kW

A shaft transmits 90 kW at 900 rpm. Find the torque T in the shaft.

P = 90 kWn = 900 rpm
T = N·m
5.Hard
θ = 15°vs = 5 m

A solid sphere starts from rest and rolls without slipping down a slope inclined at 15° to the horizontal. Use g = 9.81 m/s². Find its speed v after it has rolled 5 m along the slope.

θ = 15°s = 5 mI = (2/5)·m·r²g = 9.81 m/s²
v = m/s
6.Hard
7 m/sω

A solid sphere of mass 0.5 kg rolls without slipping at 7 m/s. Find its rotational kinetic energy Erot.

m = 0.5 kgv = 7 m/sI = (2/5)·m·r²
Erot = J

Answer key

  1. 1. Ek = 268.7 kJ
  2. 2. Ek = 495.2 kJ
  3. 3. v = 4.407 m/s
  4. 4. T = 954.9 N·m
  5. 5. v = 4.259 m/s
  6. 6. Erot = 4.9 J

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