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 = 0.45 mn = 300 rpm270 kg

A flywheel of mass 270 kg has a radius of gyration of 0.45 m about its axis. It spins at 300 rpm. Find its kinetic energy Ek in kJ.

M = 270 kgk = 0.45 mn = 300 rpm
Ek = kJ
2.Easy
Or = 0.1 mL = 0.7 m0.8 m2.5 kg10 kg

A pendulum is made of a uniform slender rod (2.5 kg, 0.7 m long) pivoted at its top end O, with a thin solid disc of mass 10 kg and radius 0.1 m fixed to its lower end. The disc swings in its own plane and its centre is 0.8 m below O. Find the mass moment of inertia IO of the pendulum about O.

mrod = 2.5 kgL = 0.7 mmdisc = 10 kgr = 0.1 md = 0.8 m
IO = kg·m²
3.Medium
L = 0.7 mm = 2 kgα

A uniform slender rod of mass 2 kg and length 0.7 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 = 2 kgL = 0.7 mg = 9.81 m/s²
R = N
4.Medium
v = ?L = 2.2 mm = 4.5 kg

A uniform slender rod of mass 4.5 kg and length 2.2 m is pinned at one end and released from rest in a horizontal position. Ignore friction and use g = 9.81 m/s². Find the speed v of the free end as the rod swings through the vertical position.

m = 4.5 kgL = 2.2 mg = 9.81 m/s²
v = m/s
5.Hard
100 m/s20 g0.47 mL = 0.8 m1.5 kgφ

A uniform slender rod of mass 1.5 kg and length 0.8 m hangs at rest from a frictionless pivot at its top end. A 20 g bullet moving horizontally at 100 m/s hits the rod 0.47 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 = 1.5 kgL = 0.8 mm = 20 gv = 100 m/sd = 0.47 mg = 9.81 m/s²
φ = °
6.Hard
0.6 m0.25 mn1​ = 45 rpm

A person stands on a frictionless turntable and holds a 5.5 kg dumbbell in each hand, 0.6 m from the axis. The person and turntable alone have a moment of inertia of 3 kg·m² about the axis. They turn at 45 rpm, then pull the dumbbells in to 0.25 m from the axis. Treat the dumbbells as point masses. Find the new speed n2 in rpm.

I0 = 3 kg·m²m = 2 × 5.5 kgr1 = 0.6 mr2 = 0.25 mn1 = 45 rpm
n2 = rpm

Answer key

  1. 1. Ek = 26.98 kJ
  2. 2. IO = 6.858 kg·m²
  3. 3. R = 4.905 N
  4. 4. v = 8.046 m/s
  5. 5. φ = 39.45 °
  6. 6. n2 = 84.94 rpm

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