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 → 1300 rpm40 kg

A flywheel of mass 40 kg with a radius of gyration of 0.4 m is accelerated uniformly from rest to 1300 rpm. This takes 13 s. Ignoring friction, find the constant torque T needed.

m = 40 kgk = 0.4 mn1 = 0 rpmn2 = 1300 rpmt = 13 s
T = N·m
2.Easy
k = 0.15 m700 → 2400 rpm90 kg

A flywheel of mass 90 kg with a radius of gyration of 0.15 m is accelerated uniformly from 700 rpm to 2400 rpm. This takes 5 s. Ignoring friction, find the constant torque T needed.

m = 90 kgk = 0.15 mn1 = 700 rpmn2 = 2400 rpmt = 5 s
T = N·m
3.Medium
n = 3000 rpmTb​ = 35 N·mI = 15.5 kg·m²

A flywheel with a moment of inertia of 15.5 kg·m² spins at 3000 rpm. A brake applies a constant friction torque of 35 N·m. How long t does it take to stop?

I = 15.5 kg·m²n = 3000 rpmTb = 35 N·m
t = s
4.Medium
n = 300 rpmTb​ = 200 N·mI = 6 kg·m²

A flywheel with a moment of inertia of 6 kg·m² spins at 300 rpm. A brake applies a constant friction torque of 200 N·m. How many revolutions N does the flywheel make before it stops?

I = 6 kg·m²n = 300 rpmTb = 200 N·m
N = rev
5.Hard
400 m/s45 g0.45 mL = 0.5 m4 kg

A uniform slender rod of mass 4 kg and length 0.5 m hangs at rest from a frictionless pivot at its top end. A 45 g bullet moving horizontally at 400 m/s hits the rod 0.45 m below the pivot and stays embedded. Find the angular velocity ω of the rod just after the impact.

M = 4 kgL = 0.5 mm = 45 gv = 400 m/sd = 0.45 m
ω = rad/s
6.Hard
θ = 10°vs = 3 m

A hollow sphere starts from rest and rolls without slipping down a slope inclined at 10° to the horizontal. Use g = 9.81 m/s². Its radius is 0.3 m. Find its angular velocity ω after it has rolled 3 m along the slope.

θ = 10°s = 3 mI = (2/3)·m·r²g = 9.81 m/s²r = 0.3 m
ω = rad/s

Answer key

  1. 1. T = 67.02 N·m
  2. 2. T = 72.1 N·m
  3. 3. t = 139.1 s
  4. 4. N = 2.356 rev
  5. 5. ω = 23.65 rad/s
  6. 6. ω = 8.255 rad/s

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