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
R = 0.5 mn = 2900 rpm260 kg

A flywheel is a uniform solid disc of mass 260 kg and radius 0.5 m. It spins at 2900 rpm. Find its kinetic energy Ek in kJ.

M = 260 kgR = 0.5 mn = 2900 rpm
Ek = kJ
2.Easy
k = 0.1 m500 → 800 rpm140 kg

A flywheel of mass 140 kg with a radius of gyration of 0.1 m is accelerated uniformly from 500 rpm to 800 rpm. The driving torque is a constant 1.8 N·m and friction can be ignored. How long t does this take?

m = 140 kgk = 0.1 mn1 = 500 rpmn2 = 800 rpmT = 1.8 N·m
t = s
3.Medium
0 → 500 rpmI = 39 kg·m²

A motor brings a flywheel with a moment of inertia of 39 kg·m² from rest up to 500 rpm in 52 s. Ignoring losses, find the average power Pavg it delivers, in kW.

I = 39 kg·m²n = 500 rpmt = 52 s
Pavg = kW
4.Medium
7.5 kgaαM = 4.5 kgR = 0.45 m

A 7.5 kg block hangs from a light cord wrapped around a pulley, a uniform solid disc of mass 4.5 kg and radius 0.45 m that turns on a frictionless horizontal axle. The block is released from rest. Use g = 9.81 m/s². Find the speed v of the block after it has fallen 4 m.

m = 7.5 kgM = 4.5 kgR = 0.45 mg = 9.81 m/s²h = 4 m
v = m/s
5.Hard
120 m/s30 g0.38 mL = 0.7 m10 kg

A uniform slender rod of mass 10 kg and length 0.7 m hangs at rest from a frictionless pivot at its top end. A 30 g bullet moving horizontally at 120 m/s hits the rod 0.38 m below the pivot and stays embedded. Find the angular velocity ω of the rod just after the impact.

M = 10 kgL = 0.7 mm = 30 gv = 120 m/sd = 0.38 m
ω = rad/s
6.Hard
disc: 39 kgring: 4 kgn1​ = 1150 rpm

A uniform solid disc (mass 39 kg, radius 0.4 m) spins freely at 1150 rpm about a vertical frictionless shaft. A thin ring of mass 4 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 = 39 kgMring = 4 kgR = 0.4 mn1 = 1150 rpm
n2 = rpm

Answer key

  1. 1. Ek = 1499 kJ
  2. 2. t = 24.43 s
  3. 3. Pavg = 1.028 kW
  4. 4. v = 7.77 m/s
  5. 5. ω = 0.8353 rad/s
  6. 6. n2 = 954.3 rpm

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