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 = 0.3 m0 → 2000 rpm180 kg

A flywheel of mass 180 kg with a radius of gyration of 0.3 m is accelerated uniformly from rest to 2000 rpm. The driving torque is a constant 140 N·m and friction can be ignored. How long t does this take?

m = 180 kgk = 0.3 mn1 = 0 rpmn2 = 2000 rpmT = 140 N·m
t = s
2.Easy
R = 0.55 mn = 400 rpm260 kg

A flywheel is a uniform solid disc of mass 260 kg and radius 0.55 m. It spins at 400 rpm. Find its kinetic energy Ek in kJ.

M = 260 kgR = 0.55 mn = 400 rpm
Ek = kJ
3.Medium
n = 2100 rpmTb​ = 155 N·mI = 20.5 kg·m²

A flywheel with a moment of inertia of 20.5 kg·m² spins at 2100 rpm. A brake applies a constant friction torque of 155 N·m. How long t does it take to stop?

I = 20.5 kg·m²n = 2100 rpmTb = 155 N·m
t = s
4.Medium
n = 800 rpmTb​ = 150 N·mI = 23 kg·m²

A flywheel with a moment of inertia of 23 kg·m² spins at 800 rpm. A brake applies a constant friction torque of 150 N·m. How many revolutions N does the flywheel make before it stops?

I = 23 kg·m²n = 800 rpmTb = 150 N·m
N = rev
5.Hard
0.6 m0.15 mn1​ = 35 rpm

A person stands on a frictionless turntable and holds a 2 kg dumbbell in each hand, 0.6 m from the axis. The person and turntable alone have a moment of inertia of 5 kg·m² about the axis. They turn at 35 rpm, then pull the dumbbells in to 0.15 m from the axis. Treat the dumbbells as point masses. Find the new speed n2 in rpm.

I0 = 5 kg·m²m = 2 × 2 kgr1 = 0.6 mr2 = 0.15 mn1 = 35 rpm
n2 = rpm
6.Hard
disc: 32 kgring: 1 kgn1​ = 800 rpm

A uniform solid disc (mass 32 kg, radius 0.25 m) spins freely at 800 rpm about a vertical frictionless shaft. A thin ring of mass 1 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 = 32 kgMring = 1 kgR = 0.25 mn1 = 800 rpm
ΔE = J

Answer key

  1. 1. t = 24.24 s
  2. 2. Ek = 34.5 kJ
  3. 3. t = 29.09 s
  4. 4. N = 85.64 rev
  5. 5. n2 = 44.28 rpm
  6. 6. ΔE = 206.4 J

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