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 = 0.4 m0 → 200 rpm180 kg

A flywheel of mass 180 kg with a radius of gyration of 0.4 m is accelerated uniformly from rest to 200 rpm. This takes 28 s. Ignoring friction, find the constant torque T needed.

m = 180 kgk = 0.4 mn1 = 0 rpmn2 = 200 rpmt = 28 s
T = N·m
2.Easy
k = 0.15 m0 → 900 rpm90 kg

A flywheel of mass 90 kg with a radius of gyration of 0.15 m is accelerated uniformly from rest to 900 rpm. The driving torque is a constant 6.6 N·m and friction can be ignored. How long t does this take?

m = 90 kgk = 0.15 mn1 = 0 rpmn2 = 900 rpmT = 6.6 N·m
t = s
3.Medium
n = 700 rpmTb​ = 130 N·mI = 36 kg·m²

A flywheel with a moment of inertia of 36 kg·m² spins at 700 rpm. A brake applies a constant friction torque of 130 N·m. How many revolutions N does the flywheel make before it stops?

I = 36 kg·m²n = 700 rpmTb = 130 N·m
N = rev
4.Medium
n = 1400 rpmTb​ = 95 N·mI = 27.5 kg·m²

A flywheel with a moment of inertia of 27.5 kg·m² spins at 1400 rpm. A brake applies a constant friction torque of 95 N·m. How many revolutions N does the flywheel make before it stops?

I = 27.5 kg·m²n = 1400 rpmTb = 95 N·m
N = rev
5.Hard
θ = 40°vs = 3 m

A thin hoop starts from rest and rolls without slipping down a slope inclined at 40° to the horizontal. Use g = 9.81 m/s². Its radius is 0.05 m. Find its angular velocity ω after it has rolled 3 m along the slope.

θ = 40°s = 3 mI = m·r²g = 9.81 m/s²r = 0.05 m
ω = rad/s
6.Hard
θ = 15°vs = 5 m

A solid sphere starts from rest and rolls without slipping down a slope inclined at 15° to the horizontal. Use g = 9.81 m/s². Its radius is 0.25 m. Find its angular velocity ω after it has rolled 5 m along the slope.

θ = 15°s = 5 mI = (2/5)·m·r²g = 9.81 m/s²r = 0.25 m
ω = rad/s

Answer key

  1. 1. T = 21.54 N·m
  2. 2. t = 28.92 s
  3. 3. N = 118.4 rev
  4. 4. N = 495.1 rev
  5. 5. ω = 86.99 rad/s
  6. 6. ω = 17.03 rad/s

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