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 = 0.35 mn = 1400 rpm210 kg

A flywheel of mass 210 kg has a radius of gyration of 0.35 m about its axis. It spins at 1400 rpm. Find its kinetic energy Ek in kJ.

M = 210 kgk = 0.35 mn = 1400 rpm
Ek = kJ
2.Easy
k = 0.3 m400 → 1300 rpm40 kg

A flywheel of mass 40 kg with a radius of gyration of 0.3 m is accelerated uniformly from 400 rpm to 1300 rpm. This takes 14 s. Ignoring friction, find the constant torque T needed.

m = 40 kgk = 0.3 mn1 = 400 rpmn2 = 1300 rpmt = 14 s
T = N·m
3.Medium
v = ?1 kgL = 2.3 mm = 7 kg

A uniform slender rod of mass 7 kg and length 2.3 m is pinned at one end and released from rest in a horizontal position. A small ball of mass 1 kg is fixed to its free end. 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 = 7 kgL = 2.3 mmball = 1 kgg = 9.81 m/s²
v = m/s
4.Medium
14 kgaαM = 6 kgR = 0.35 m

A 14 kg block hangs from a light cord wrapped around a pulley, a uniform solid disc of mass 6 kg and radius 0.35 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 = 14 kgM = 6 kgR = 0.35 mg = 9.81 m/s²
T = N
5.Hard
θ = 25°as = 4 m

A thin hoop rolls without slipping down a slope inclined at 25° to the horizontal. Use g = 9.81 m/s². It starts from rest. How long t does it take to roll 4 m down the slope?

θ = 25°I = m·r²g = 9.81 m/s²s = 4 m
t = s
6.Hard
0.85 m0.15 mn1​ = 50 rpm

A person stands on a frictionless turntable and holds a 1 kg dumbbell in each hand, 0.85 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 50 rpm, then pull the dumbbells in to 0.15 m from the axis. Treat the dumbbells as point masses. Find the new speed n2 in rpm.

I0 = 3.5 kg·m²m = 2 × 1 kgr1 = 0.85 mr2 = 0.15 mn1 = 50 rpm
n2 = rpm

Answer key

  1. 1. Ek = 276.5 kJ
  2. 2. T = 24.24 N·m
  3. 3. v = 7.805 m/s
  4. 4. T = 24.24 N
  5. 5. t = 1.964 s
  6. 6. n2 = 69.75 rpm

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