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 = 0.3 mn = 500 rpm60 kg

A flywheel of mass 60 kg has a radius of gyration of 0.3 m about its axis. It spins at 500 rpm. Find its kinetic energy Ek in kJ.

M = 60 kgk = 0.3 mn = 500 rpm
Ek = kJ
2.Easy
R = 0.3 mn = 1500 rpm20 kg

A flywheel is a uniform solid disc of mass 20 kg and radius 0.3 m. It spins at 1500 rpm. Find its kinetic energy Ek in kJ.

M = 20 kgR = 0.3 mn = 1500 rpm
Ek = kJ
3.Medium
n = 1100 rpmT = 990 N·m

A motor delivers a torque of 990 N·m at 1100 rpm. Find its power output P in kW.

T = 990 N·mn = 1100 rpm
P = kW
4.Medium
L = 0.9 mm = 7 kgα

A uniform slender rod of mass 7 kg and length 0.9 m is pinned at one end and held horizontal. It is released from rest. Use g = 9.81 m/s². Find the vertical force R that the pin exerts on the rod just after release.

m = 7 kgL = 0.9 mg = 9.81 m/s²
R = N
5.Hard
θ = 20°vs = 9.5 m

A thin hoop starts from rest and rolls without slipping down a slope inclined at 20° to the horizontal. Use g = 9.81 m/s². Find its speed v after it has rolled 9.5 m along the slope.

θ = 20°s = 9.5 mI = m·r²g = 9.81 m/s²
v = m/s
6.Hard
θ = 20°vs = 7 m

A solid cylinder starts from rest and rolls without slipping down a slope inclined at 20° to the horizontal. Use g = 9.81 m/s². Find its speed v after it has rolled 7 m along the slope.

θ = 20°s = 7 mI = ½·m·r²g = 9.81 m/s²
v = m/s

Answer key

  1. 1. Ek = 7.402 kJ
  2. 2. Ek = 11.1 kJ
  3. 3. P = 114 kW
  4. 4. R = 17.17 N
  5. 5. v = 5.646 m/s
  6. 6. v = 5.596 m/s

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