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
L = 0.7 mGOd = 0.2 mm = 7.5 kg

A uniform slender rod of mass 7.5 kg and length 0.7 m rotates about an axis O perpendicular to the rod, 0.2 m from its centre G. Find its mass moment of inertia IO about that axis.

m = 7.5 kgL = 0.7 md = 0.2 m
IO = kg·m²
2.Easy
k = 0.25 m0 → 1000 rpm160 kg

A flywheel of mass 160 kg with a radius of gyration of 0.25 m is accelerated uniformly from rest to 1000 rpm. The driving torque is a constant 46 N·m and friction can be ignored. How long t does this take?

m = 160 kgk = 0.25 mn1 = 0 rpmn2 = 1000 rpmT = 46 N·m
t = s
3.Medium
v = ?5 kgL = 2.3 mm = 2.5 kg

A uniform slender rod of mass 2.5 kg and length 2.3 m is pinned at one end and released from rest in a horizontal position. A small ball of mass 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 = 2.5 kgL = 2.3 mmball = 5 kgg = 9.81 m/s²
v = m/s
4.Medium
7.5 kgaαM = 3 kgR = 0.4 m

A 7.5 kg block hangs from a light cord wrapped around a pulley, a uniform solid disc of mass 3 kg and radius 0.4 m that turns on a frictionless horizontal axle. The block is released from rest. Use g = 9.81 m/s². Find the acceleration a of the block.

m = 7.5 kgM = 3 kgR = 0.4 mg = 9.81 m/s²
a = m/s²
5.Hard
disc: 12 kgring: 16 kgn1​ = 250 rpm

A uniform solid disc (mass 12 kg, radius 0.25 m) spins freely at 250 rpm about a vertical frictionless shaft. A thin ring of mass 16 kg and the same radius is dropped onto it from rest, centred on the shaft, and the two quickly spin together. How much kinetic energy ΔE is lost in the process?

Mdisc = 12 kgMring = 16 kgR = 0.25 mn1 = 250 rpm
ΔE = J
6.Hard
θ = 10°vs = 2 m

A solid cylinder starts from rest and rolls without slipping down a slope inclined at 10° to the horizontal. Use g = 9.81 m/s². Find its speed v after it has rolled 2 m along the slope.

θ = 10°s = 2 mI = ½·m·r²g = 9.81 m/s²
v = m/s

Answer key

  1. 1. IO = 0.6062 kg·m²
  2. 2. t = 22.77 s
  3. 3. v = 6.953 m/s
  4. 4. a = 8.175 m/s²
  5. 5. ΔE = 93.46 J
  6. 6. v = 2.131 m/s

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