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 = 0.5 m0 → 500 rpm70 kg

A flywheel of mass 70 kg with a radius of gyration of 0.5 m is accelerated uniformly from rest to 500 rpm. This takes 26 s. Ignoring friction, find the constant torque T needed.

m = 70 kgk = 0.5 mn1 = 0 rpmn2 = 500 rpmt = 26 s
T = N·m
2.Easy
Or = 0.05 mL = 0.4 m0.45 m1 kg4 kg

A pendulum is made of a uniform slender rod (1 kg, 0.4 m long) pivoted at its top end O, with a solid sphere of mass 4 kg and radius 0.05 m fixed to its lower end. The centre of the sphere is 0.45 m below O. Find the mass moment of inertia IO of the pendulum about O.

mrod = 1 kgL = 0.4 mmsphere = 4 kgr = 0.05 md = 0.45 m
IO = kg·m²
3.Medium
L = 0.8 mm = 17.5 kgα

A uniform slender rod of mass 17.5 kg and length 0.8 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 = 17.5 kgL = 0.8 mg = 9.81 m/s²
R = N
4.Medium
n = 2700 rpmTb​ = 45 N·mI = 31 kg·m²

A flywheel with a moment of inertia of 31 kg·m² spins at 2700 rpm. A brake applies a constant friction torque of 45 N·m. How long t does it take to stop?

I = 31 kg·m²n = 2700 rpmTb = 45 N·m
t = s
5.Hard
160 m/s15 g1.18 mL = 1.2 m7 kgφ

A uniform slender rod of mass 7 kg and length 1.2 m hangs at rest from a frictionless pivot at its top end. A 15 g bullet moving horizontally at 160 m/s hits the rod 1.18 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 = 7 kgL = 1.2 mm = 15 gv = 160 m/sd = 1.18 mg = 9.81 m/s²
φ = °
6.Hard
θ = 25°a

A hollow sphere rolls without slipping down a slope inclined at 25° to the horizontal. Use g = 9.81 m/s². Find the acceleration a of its centre.

θ = 25°I = (2/3)·m·r²g = 9.81 m/s²
a = m/s²

Answer key

  1. 1. T = 35.24 N·m
  2. 2. IO = 0.8673 kg·m²
  3. 3. R = 42.92 N
  4. 4. t = 194.8 s
  5. 5. φ = 13.75 °
  6. 6. a = 2.488 m/s²

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