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
R = 0.55 mn = 2900 rpm20 kg

A flywheel is a uniform solid disc of mass 20 kg and radius 0.55 m. It spins at 2900 rpm. Find its kinetic energy Ek in kJ.

M = 20 kgR = 0.55 mn = 2900 rpm
Ek = kJ
2.Easy
R = 0.55 mn = 1400 rpm200 kg

A flywheel is a uniform solid disc of mass 200 kg and radius 0.55 m. It spins at 1400 rpm. Find its kinetic energy Ek in kJ.

M = 200 kgR = 0.55 mn = 1400 rpm
Ek = kJ
3.Medium
n = 1800 rpmTb​ = 155 N·mI = 1.5 kg·m²

A flywheel with a moment of inertia of 1.5 kg·m² spins at 1800 rpm. A brake applies a constant friction torque of 155 N·m. How long t does it take to stop?

I = 1.5 kg·m²n = 1800 rpmTb = 155 N·m
t = s
4.Medium
v = ?L = 2.4 mm = 3 kg

A uniform slender rod of mass 3 kg and length 2.4 m is pinned at one end and released from rest in a horizontal position. Ignore friction and use g = 9.81 m/s². Find the speed v of the free end as the rod swings through the vertical position.

m = 3 kgL = 2.4 mg = 9.81 m/s²
v = m/s
5.Hard
θ = 10°as = 5 m

A thin hoop rolls without slipping down a slope inclined at 10° to the horizontal. Use g = 9.81 m/s². It starts from rest. How long t does it take to roll 5 m down the slope?

θ = 10°I = m·r²g = 9.81 m/s²s = 5 m
t = s
6.Hard
540 m/s45 g0.91 mL = 1.4 m7 kgφ

A uniform slender rod of mass 7 kg and length 1.4 m hangs at rest from a frictionless pivot at its top end. A 45 g bullet moving horizontally at 540 m/s hits the rod 0.91 m below the pivot and stays embedded. Use g = 9.81 m/s². Find the largest angle φ from the vertical through which the rod swings.

M = 7 kgL = 1.4 mm = 45 gv = 540 m/sd = 0.91 mg = 9.81 m/s²
φ = °

Answer key

  1. 1. Ek = 139.5 kJ
  2. 2. Ek = 325.1 kJ
  3. 3. t = 1.824 s
  4. 4. v = 8.404 m/s
  5. 5. t = 3.426 s
  6. 6. φ = 95.4 °

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