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 m600 → 1500 rpm30 kg

A flywheel of mass 30 kg with a radius of gyration of 0.4 m is accelerated uniformly from 600 rpm to 1500 rpm. This takes 30 s. Ignoring friction, find the constant torque T needed.

m = 30 kgk = 0.4 mn1 = 600 rpmn2 = 1500 rpmt = 30 s
T = N·m
2.Easy
k = 0.35 mn = 2400 rpm50 kg

A flywheel of mass 50 kg has a radius of gyration of 0.35 m about its axis. It spins at 2400 rpm. Find its kinetic energy Ek in kJ.

M = 50 kgk = 0.35 mn = 2400 rpm
Ek = kJ
3.Medium
n = 1600 rpmT = 1540 N·m

A motor delivers a torque of 1540 N·m at 1600 rpm. Find its power output P in kW.

T = 1540 N·mn = 1600 rpm
P = kW
4.Medium
n = 600 rpmP = 8 kW

A shaft transmits 8 kW at 600 rpm. Find the torque T in the shaft.

P = 8 kWn = 600 rpm
T = N·m
5.Hard
520 m/s20 g1.55 mL = 2 m7.5 kgφ

A uniform slender rod of mass 7.5 kg and length 2 m hangs at rest from a frictionless pivot at its top end. A 20 g bullet moving horizontally at 520 m/s hits the rod 1.55 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 = 7.5 kgL = 2 mm = 20 gv = 520 m/sd = 1.55 mg = 9.81 m/s²
φ = °
6.Hard
3.5 m/sω

A solid cylinder of mass 5.5 kg rolls without slipping at 3.5 m/s. What percentage p of its total kinetic energy is rotational?

m = 5.5 kgv = 3.5 m/sI = ½·m·r²
p = %

Answer key

  1. 1. T = 15.08 N·m
  2. 2. Ek = 193.4 kJ
  3. 3. P = 258 kW
  4. 4. T = 127.3 N·m
  5. 5. φ = 34.41 °
  6. 6. p = 33.33 %

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