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 = 0.1 m0 → 1400 rpm40 kg

A flywheel of mass 40 kg with a radius of gyration of 0.1 m is accelerated uniformly from rest to 1400 rpm. This takes 12 s. Ignoring friction, find the constant torque T needed.

m = 40 kgk = 0.1 mn1 = 0 rpmn2 = 1400 rpmt = 12 s
T = N·m
2.Easy
k = 0.1 m0 → 1600 rpm100 kg

A flywheel of mass 100 kg with a radius of gyration of 0.1 m is accelerated uniformly from rest to 1600 rpm. The driving torque is a constant 6.4 N·m and friction can be ignored. How long t does this take?

m = 100 kgk = 0.1 mn1 = 0 rpmn2 = 1600 rpmT = 6.4 N·m
t = s
3.Medium
n = 1400 rpmTb​ = 85 N·mI = 21.5 kg·m²

A flywheel with a moment of inertia of 21.5 kg·m² spins at 1400 rpm. A brake applies a constant friction torque of 85 N·m. How long t does it take to stop?

I = 21.5 kg·m²n = 1400 rpmTb = 85 N·m
t = s
4.Medium
L = 1.2 mm = 14 kgα

A uniform slender rod of mass 14 kg and length 1.2 m is pinned at one end and held horizontal. It is released from rest. Use g = 9.81 m/s². Find its angular acceleration α just after release.

m = 14 kgL = 1.2 mg = 9.81 m/s²
α = rad/s²
5.Hard
0.6 m0.25 mn1​ = 20 rpm

A person stands on a frictionless turntable and holds a 3.5 kg dumbbell in each hand, 0.6 m from the axis. The person and turntable alone have a moment of inertia of 4 kg·m² about the axis. They turn at 20 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 = 4 kg·m²m = 2 × 3.5 kgr1 = 0.6 mr2 = 0.25 mn1 = 20 rpm
n2 = rpm
6.Hard
θ = 25°a

A solid cylinder 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 = ½·m·r²g = 9.81 m/s²
a = m/s²

Answer key

  1. 1. T = 4.887 N·m
  2. 2. t = 26.18 s
  3. 3. t = 37.08 s
  4. 4. α = 12.26 rad/s²
  5. 5. n2 = 29.39 rpm
  6. 6. a = 2.764 m/s²

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