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 = 0.6 m0 → 700 rpm170 kg

A flywheel of mass 170 kg with a radius of gyration of 0.6 m is accelerated uniformly from rest to 700 rpm. The driving torque is a constant 500 N·m and friction can be ignored. How long t does this take?

m = 170 kgk = 0.6 mn1 = 0 rpmn2 = 700 rpmT = 500 N·m
t = s
2.Easy
k = 0.45 mn = 1500 rpm240 kg

A flywheel of mass 240 kg has a radius of gyration of 0.45 m about its axis. It spins at 1500 rpm. Find its kinetic energy Ek in kJ.

M = 240 kgk = 0.45 mn = 1500 rpm
Ek = kJ
3.Medium
n = 1200 rpmTb​ = 160 N·mI = 40 kg·m²

A flywheel with a moment of inertia of 40 kg·m² spins at 1200 rpm. A brake applies a constant friction torque of 160 N·m. How long t does it take to stop?

I = 40 kg·m²n = 1200 rpmTb = 160 N·m
t = s
4.Medium
n = 2700 rpmP = 3.5 kW

A shaft transmits 3.5 kW at 2700 rpm. Find the torque T in the shaft.

P = 3.5 kWn = 2700 rpm
T = N·m
5.Hard
θ = 30°a

A solid sphere rolls without slipping down a slope inclined at 30° to the horizontal. Use g = 9.81 m/s². Find the smallest coefficient of static friction μs that prevents it from slipping.

θ = 30°I = (2/5)·m·r²g = 9.81 m/s²
μs =
6.Hard
3 m/sω

A thin hoop of mass 1 kg rolls without slipping at 3 m/s. Find its rotational kinetic energy Erot.

m = 1 kgv = 3 m/sI = m·r²
Erot = J

Answer key

  1. 1. t = 8.972 s
  2. 2. Ek = 599.6 kJ
  3. 3. t = 31.42 s
  4. 4. T = 12.38 N·m
  5. 5. μs = 0.165
  6. 6. Erot = 4.5 J

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