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 = 0.2 mn = 2100 rpm230 kg

A flywheel of mass 230 kg has a radius of gyration of 0.2 m about its axis. It spins at 2100 rpm. Find its kinetic energy Ek in kJ.

M = 230 kgk = 0.2 mn = 2100 rpm
Ek = kJ
2.Easy
R = 0.6 mn = 600 rpm120 kg

A flywheel is a uniform solid disc of mass 120 kg and radius 0.6 m. It spins at 600 rpm. Find its kinetic energy Ek in kJ.

M = 120 kgR = 0.6 mn = 600 rpm
Ek = kJ
3.Medium
n = 1700 rpmP = 155 kW

A shaft transmits 155 kW at 1700 rpm. Find the torque T in the shaft.

P = 155 kWn = 1700 rpm
T = N·m
4.Medium
v = ?1 kgL = 2.4 mm = 2 kg

A uniform slender rod of mass 2 kg and length 2.4 m is pinned at one end and released from rest in a horizontal position. A small ball of mass 1 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 = 2 kgL = 2.4 mmball = 1 kgg = 9.81 m/s²
v = m/s
5.Hard
θ = 25°a

A hollow sphere rolls without slipping down a slope inclined at 25° to the horizontal. Use g = 9.81 m/s². Find the smallest coefficient of static friction μs that prevents it from slipping.

θ = 25°I = (2/3)·m·r²g = 9.81 m/s²
μs =
6.Hard
9.5 m/sω

A hollow sphere of mass 11.5 kg rolls without slipping at 9.5 m/s. What percentage p of its total kinetic energy is rotational?

m = 11.5 kgv = 9.5 m/sI = (2/3)·m·r²
p = %

Answer key

  1. 1. Ek = 222.5 kJ
  2. 2. Ek = 42.64 kJ
  3. 3. T = 870.7 N·m
  4. 4. v = 7.517 m/s
  5. 5. μs = 0.1865
  6. 6. p = 40 %

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