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 = 0.2 mn = 1000 rpm140 kg

A flywheel is a uniform solid disc of mass 140 kg and radius 0.2 m. It spins at 1000 rpm. Find its kinetic energy Ek in kJ.

M = 140 kgR = 0.2 mn = 1000 rpm
Ek = kJ
2.Easy
k = 0.45 m0 → 1000 rpm100 kg

A flywheel of mass 100 kg with a radius of gyration of 0.45 m is accelerated uniformly from rest to 1000 rpm. This takes 30 s. Ignoring friction, find the constant torque T needed.

m = 100 kgk = 0.45 mn1 = 0 rpmn2 = 1000 rpmt = 30 s
T = N·m
3.Medium
10 kgaαM = 8.5 kgR = 0.4 m

A 10 kg block hangs from a light cord wrapped around a pulley, a uniform solid disc of mass 8.5 kg and radius 0.4 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 = 10 kgM = 8.5 kgR = 0.4 mg = 9.81 m/s²
T = N
4.Medium
n = 2900 rpmTb​ = 115 N·mI = 27.5 kg·m²

A flywheel with a moment of inertia of 27.5 kg·m² spins at 2900 rpm. A brake applies a constant friction torque of 115 N·m. How long t does it take to stop?

I = 27.5 kg·m²n = 2900 rpmTb = 115 N·m
t = s
5.Hard
360 m/s10 g0.6 mL = 1.5 m1.5 kg

A uniform slender rod of mass 1.5 kg and length 1.5 m hangs at rest from a frictionless pivot at its top end. A 10 g bullet moving horizontally at 360 m/s hits the rod 0.6 m below the pivot and stays embedded. Find the angular velocity ω of the rod just after the impact.

M = 1.5 kgL = 1.5 mm = 10 gv = 360 m/sd = 0.6 m
ω = rad/s
6.Hard
340 m/s50 g0.49 mL = 0.6 m2.5 kg

A uniform slender rod of mass 2.5 kg and length 0.6 m hangs at rest from a frictionless pivot at its top end. A 50 g bullet moving horizontally at 340 m/s hits the rod 0.49 m below the pivot and stays embedded. Find the angular velocity ω of the rod just after the impact.

M = 2.5 kgL = 0.6 mm = 50 gv = 340 m/sd = 0.49 m
ω = rad/s

Answer key

  1. 1. Ek = 15.35 kJ
  2. 2. T = 70.69 N·m
  3. 3. T = 29.26 N
  4. 4. t = 72.62 s
  5. 5. ω = 1.914 rad/s
  6. 6. ω = 26.7 rad/s

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