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 → 400 rpm150 kg

A flywheel of mass 150 kg with a radius of gyration of 0.6 m is accelerated uniformly from rest to 400 rpm. The driving torque is a constant 210 N·m and friction can be ignored. How long t does this take?

m = 150 kgk = 0.6 mn1 = 0 rpmn2 = 400 rpmT = 210 N·m
t = s
2.Easy
R = 0.5 mn = 2600 rpm250 kg

A flywheel is a uniform solid disc of mass 250 kg and radius 0.5 m. It spins at 2600 rpm. Find its kinetic energy Ek in kJ.

M = 250 kgR = 0.5 mn = 2600 rpm
Ek = kJ
3.Medium
n = 1100 rpmTb​ = 60 N·mI = 4 kg·m²

A flywheel with a moment of inertia of 4 kg·m² spins at 1100 rpm. A brake applies a constant friction torque of 60 N·m. How long t does it take to stop?

I = 4 kg·m²n = 1100 rpmTb = 60 N·m
t = s
4.Medium
12 kgaαM = 19.5 kgR = 0.4 m

A 12 kg block hangs from a light cord wrapped around a pulley, a uniform solid disc of mass 19.5 kg and radius 0.4 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 = 12 kgM = 19.5 kgR = 0.4 mg = 9.81 m/s²
T = N
5.Hard
θ = 25°vs = 9 m

A thin hoop starts from rest and rolls without slipping down a slope inclined at 25° to the horizontal. Use g = 9.81 m/s². Its radius is 0.05 m. Find its angular velocity ω after it has rolled 9 m along the slope.

θ = 25°s = 9 mI = m·r²g = 9.81 m/s²r = 0.05 m
ω = rad/s
6.Hard
θ = 10°vs = 7 m

A thin hoop starts from rest and rolls without slipping down a slope inclined at 10° to the horizontal. Use g = 9.81 m/s². Find its speed v after it has rolled 7 m along the slope.

θ = 10°s = 7 mI = m·r²g = 9.81 m/s²
v = m/s

Answer key

  1. 1. t = 10.77 s
  2. 2. Ek = 1158 kJ
  3. 3. t = 7.679 s
  4. 4. T = 52.77 N
  5. 5. ω = 122.2 rad/s
  6. 6. v = 3.453 m/s

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