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 = 0.6 m700 → 1600 rpm80 kg

A flywheel of mass 80 kg with a radius of gyration of 0.6 m is accelerated uniformly from 700 rpm to 1600 rpm. This takes 24 s. Ignoring friction, find the constant torque T needed.

m = 80 kgk = 0.6 mn1 = 700 rpmn2 = 1600 rpmt = 24 s
T = N·m
2.Easy
R = 0.45 mn = 2000 rpm40 kg

A flywheel is a uniform solid disc of mass 40 kg and radius 0.45 m. It spins at 2000 rpm. Find its kinetic energy Ek in kJ.

M = 40 kgR = 0.45 mn = 2000 rpm
Ek = kJ
3.Medium
L = 2.4 mm = 9 kgα

A uniform slender rod of mass 9 kg and length 2.4 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 = 9 kgL = 2.4 mg = 9.81 m/s²
R = N
4.Medium
6 kgaαM = 9 kgR = 0.2 m

A 6 kg block hangs from a light cord wrapped around a pulley, a uniform solid disc of mass 9 kg and radius 0.2 m that turns on a frictionless horizontal axle. The block is released from rest. Use g = 9.81 m/s². Find the tension T in the cord.

m = 6 kgM = 9 kgR = 0.2 mg = 9.81 m/s²
T = N
5.Hard
θ = 25°vs = 10 m

A thin hoop starts from rest and rolls without slipping down a slope inclined at 25° to the horizontal. Use g = 9.81 m/s². Its radius is 0.2 m. Find its angular velocity ω after it has rolled 10 m along the slope.

θ = 25°s = 10 mI = m·r²g = 9.81 m/s²r = 0.2 m
ω = rad/s
6.Hard
disc: 2 kgring: 19 kgn1​ = 1200 rpm

A uniform solid disc (mass 2 kg, radius 0.3 m) spins freely at 1200 rpm about a vertical frictionless shaft. A thin ring of mass 19 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 = 2 kgMring = 19 kgR = 0.3 mn1 = 1200 rpm
ΔE = J

Answer key

  1. 1. T = 113.1 N·m
  2. 2. Ek = 88.83 kJ
  3. 3. R = 22.07 N
  4. 4. T = 25.23 N
  5. 5. ω = 32.19 rad/s
  6. 6. ΔE = 675.1 J

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