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 = 0.6 mGOd = 0.15 mm = 7 kg

A uniform slender rod of mass 7 kg and length 0.6 m rotates about an axis O perpendicular to the rod, 0.15 m from its centre G. Find its mass moment of inertia IO about that axis.

m = 7 kgL = 0.6 md = 0.15 m
IO = kg·m²
2.Easy
k = 0.15 m800 → 1900 rpm120 kg

A flywheel of mass 120 kg with a radius of gyration of 0.15 m is accelerated uniformly from 800 rpm to 1900 rpm. This takes 18 s. Ignoring friction, find the constant torque T needed.

m = 120 kgk = 0.15 mn1 = 800 rpmn2 = 1900 rpmt = 18 s
T = N·m
3.Medium
n = 1100 rpmT = 1260 N·m

A motor delivers a torque of 1260 N·m at 1100 rpm. Find its power output P in kW.

T = 1260 N·mn = 1100 rpm
P = kW
4.Medium
v = ?L = 1.1 mm = 8 kg

A uniform slender rod of mass 8 kg and length 1.1 m is pinned at one end and released from rest in a horizontal position. 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 = 8 kgL = 1.1 mg = 9.81 m/s²
v = m/s
5.Hard
disc: 24 kgring: 17 kgn1​ = 1150 rpm

A uniform solid disc (mass 24 kg, radius 0.1 m) spins freely at 1150 rpm about a vertical frictionless shaft. A thin ring of mass 17 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 = 24 kgMring = 17 kgR = 0.1 mn1 = 1150 rpm
n2 = rpm
6.Hard
θ = 25°vs = 5.5 m

A solid sphere starts from rest and rolls without slipping down a slope inclined at 25° to the horizontal. Use g = 9.81 m/s². Find its speed v after it has rolled 5.5 m along the slope.

θ = 25°s = 5.5 mI = (2/5)·m·r²g = 9.81 m/s²
v = m/s

Answer key

  1. 1. IO = 0.3675 kg·m²
  2. 2. T = 17.28 N·m
  3. 3. P = 145.1 kW
  4. 4. v = 5.69 m/s
  5. 5. n2 = 475.9 rpm
  6. 6. v = 5.707 m/s

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