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 = 3 mGOd = 0.55 mm = 2 kg

A uniform slender rod of mass 2 kg and length 3 m rotates about an axis O perpendicular to the rod, 0.55 m from its centre G. Find its mass moment of inertia IO about that axis.

m = 2 kgL = 3 md = 0.55 m
IO = kg·m²
2.Easy
Or = 0.15 mL = 1.1 m1.25 m4 kg9 kg

A pendulum is made of a uniform slender rod (4 kg, 1.1 m long) pivoted at its top end O, with a thin solid disc of mass 9 kg and radius 0.15 m fixed to its lower end. The disc swings in its own plane and its centre is 1.25 m below O. Find the mass moment of inertia IO of the pendulum about O.

mrod = 4 kgL = 1.1 mmdisc = 9 kgr = 0.15 md = 1.25 m
IO = kg·m²
3.Medium
ω = ?0.5 kgL = 1.5 mm = 5 kg

A uniform slender rod of mass 5 kg and length 1.5 m is pinned at one end and released from rest in a horizontal position. A small ball of mass 0.5 kg is fixed to its free end. 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 = 5 kgL = 1.5 mmball = 0.5 kgg = 9.81 m/s²
ω = rad/s
4.Medium
n = 1300 rpmT = 1520 N·m

A motor delivers a torque of 1520 N·m at 1300 rpm. Find its power output P in kW.

T = 1520 N·mn = 1300 rpm
P = kW
5.Hard
disc: 18 kgring: 7 kgn1​ = 500 rpm

A uniform solid disc (mass 18 kg, radius 0.1 m) spins freely at 500 rpm about a vertical frictionless shaft. A thin ring of mass 7 kg and the same radius is dropped onto it from rest, centred on the shaft, and the two quickly spin together. Find their common speed n2 in rpm.

Mdisc = 18 kgMring = 7 kgR = 0.1 mn1 = 500 rpm
n2 = rpm
6.Hard
θ = 15°vs = 2 m

A solid cylinder 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 2 m along the slope.

θ = 15°s = 2 mI = ½·m·r²g = 9.81 m/s²
v = m/s

Answer key

  1. 1. IO = 2.105 kg·m²
  2. 2. IO = 15.78 kg·m²
  3. 3. ω = 4.256 rad/s
  4. 4. P = 206.9 kW
  5. 5. n2 = 281.3 rpm
  6. 6. v = 2.602 m/s

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