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 = 0.25 mn = 2900 rpm60 kg

A flywheel of mass 60 kg has a radius of gyration of 0.25 m about its axis. It spins at 2900 rpm. Find its kinetic energy Ek in kJ.

M = 60 kgk = 0.25 mn = 2900 rpm
Ek = kJ
2.Easy
k = 0.2 m0 → 600 rpm180 kg

A flywheel of mass 180 kg with a radius of gyration of 0.2 m is accelerated uniformly from rest to 600 rpm. The driving torque is a constant 30 N·m and friction can be ignored. How long t does this take?

m = 180 kgk = 0.2 mn1 = 0 rpmn2 = 600 rpmT = 30 N·m
t = s
3.Medium
n = 600 rpmTb​ = 155 N·mI = 37.5 kg·m²

A flywheel with a moment of inertia of 37.5 kg·m² spins at 600 rpm. A brake applies a constant friction torque of 155 N·m. How long t does it take to stop?

I = 37.5 kg·m²n = 600 rpmTb = 155 N·m
t = s
4.Medium
2.5 kgaαM = 15.5 kgR = 0.3 m

A 2.5 kg block hangs from a light cord wrapped around a pulley, a uniform solid disc of mass 15.5 kg and radius 0.3 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 4.5 m.

m = 2.5 kgM = 15.5 kgR = 0.3 mg = 9.81 m/s²h = 4.5 m
v = m/s
5.Hard
480 m/s10 g0.43 mL = 0.7 m5.5 kgφ

A uniform slender rod of mass 5.5 kg and length 0.7 m hangs at rest from a frictionless pivot at its top end. A 10 g bullet moving horizontally at 480 m/s hits the rod 0.43 m below the pivot and stays embedded. Use g = 9.81 m/s². Find the largest angle φ from the vertical through which the rod swings.

M = 5.5 kgL = 0.7 mm = 10 gv = 480 m/sd = 0.43 mg = 9.81 m/s²
φ = °
6.Hard
0.9 m0.2 mn1​ = 55 rpm

A person stands on a frictionless turntable and holds a 2.5 kg dumbbell in each hand, 0.9 m from the axis. The person and turntable alone have a moment of inertia of 3.5 kg·m² about the axis. They turn at 55 rpm, then pull the dumbbells in to 0.2 m from the axis. Treat the dumbbells as point masses. Find the new speed n2 in rpm.

I0 = 3.5 kg·m²m = 2 × 2.5 kgr1 = 0.9 mr2 = 0.2 mn1 = 55 rpm
n2 = rpm

Answer key

  1. 1. Ek = 172.9 kJ
  2. 2. t = 15.08 s
  3. 3. t = 15.2 s
  4. 4. v = 4.64 m/s
  5. 5. φ = 28.96 °
  6. 6. n2 = 112.2 rpm

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