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 = 0.15 mn = 800 rpm300 kg

A flywheel of mass 300 kg has a radius of gyration of 0.15 m about its axis. It spins at 800 rpm. Find its kinetic energy Ek in kJ.

M = 300 kgk = 0.15 mn = 800 rpm
Ek = kJ
2.Easy
Or = 0.15 mL = 1.4 m1.55 m1 kg6 kg

A pendulum is made of a uniform slender rod (1 kg, 1.4 m long) pivoted at its top end O, with a thin solid disc of mass 6 kg and radius 0.15 m fixed to its lower end. The disc swings in its own plane and its centre is 1.55 m below O. Find the mass moment of inertia IO of the pendulum about O.

mrod = 1 kgL = 1.4 mmdisc = 6 kgr = 0.15 md = 1.55 m
IO = kg·m²
3.Medium
L = 2.5 mm = 4 kgα

A uniform slender rod of mass 4 kg and length 2.5 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 = 4 kgL = 2.5 mg = 9.81 m/s²
R = N
4.Medium
n = 600 rpmTb​ = 5 N·mI = 4.5 kg·m²

A flywheel with a moment of inertia of 4.5 kg·m² spins at 600 rpm. A brake applies a constant friction torque of 5 N·m. How many revolutions N does the flywheel make before it stops?

I = 4.5 kg·m²n = 600 rpmTb = 5 N·m
N = rev
5.Hard
θ = 20°vs = 7.5 m

A solid sphere starts from rest and rolls without slipping down a slope inclined at 20° to the horizontal. Use g = 9.81 m/s². Find its speed v after it has rolled 7.5 m along the slope.

θ = 20°s = 7.5 mI = (2/5)·m·r²g = 9.81 m/s²
v = m/s
6.Hard
0.85 m0.35 mn1​ = 30 rpm

A person stands on a frictionless turntable and holds a 3.5 kg dumbbell in each hand, 0.85 m from the axis. The person and turntable alone have a moment of inertia of 3 kg·m² about the axis. They turn at 30 rpm, then pull the dumbbells in to 0.35 m from the axis. Treat the dumbbells as point masses. Find the new speed n2 in rpm.

I0 = 3 kg·m²m = 2 × 3.5 kgr1 = 0.85 mr2 = 0.35 mn1 = 30 rpm
n2 = rpm

Answer key

  1. 1. Ek = 23.69 kJ
  2. 2. IO = 15.14 kg·m²
  3. 3. R = 9.81 N
  4. 4. N = 282.7 rev
  5. 5. v = 5.996 m/s
  6. 6. n2 = 62.66 rpm

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