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 = 0.2 m0 → 1100 rpm130 kg

A flywheel of mass 130 kg with a radius of gyration of 0.2 m is accelerated uniformly from rest to 1100 rpm. This takes 28 s. Ignoring friction, find the constant torque T needed.

m = 130 kgk = 0.2 mn1 = 0 rpmn2 = 1100 rpmt = 28 s
T = N·m
2.Easy
R = 0.8 mn = 300 rpm30 kg

A flywheel is a uniform solid disc of mass 30 kg and radius 0.8 m. It spins at 300 rpm. Find its kinetic energy Ek in kJ.

M = 30 kgR = 0.8 mn = 300 rpm
Ek = kJ
3.Medium
n = 1800 rpmT = 1110 N·m

A motor delivers a torque of 1110 N·m at 1800 rpm. Find its power output P in kW.

T = 1110 N·mn = 1800 rpm
P = kW
4.Medium
v = ?L = 2.5 mm = 6.5 kg

A uniform slender rod of mass 6.5 kg and length 2.5 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 = 6.5 kgL = 2.5 mg = 9.81 m/s²
v = m/s
5.Hard
θ = 20°vs = 1 m

A solid cylinder starts from rest and rolls without slipping down a slope inclined at 20° to the horizontal. Use g = 9.81 m/s². Its radius is 0.3 m. Find its angular velocity ω after it has rolled 1 m along the slope.

θ = 20°s = 1 mI = ½·m·r²g = 9.81 m/s²r = 0.3 m
ω = rad/s
6.Hard
480 m/s25 g0.44 mL = 0.6 m8.5 kg

A uniform slender rod of mass 8.5 kg and length 0.6 m hangs at rest from a frictionless pivot at its top end. A 25 g bullet moving horizontally at 480 m/s hits the rod 0.44 m below the pivot and stays embedded. Find the angular velocity ω of the rod just after the impact.

M = 8.5 kgL = 0.6 mm = 25 gv = 480 m/sd = 0.44 m
ω = rad/s

Answer key

  1. 1. T = 21.39 N·m
  2. 2. Ek = 4.737 kJ
  3. 3. P = 209.2 kW
  4. 4. v = 8.578 m/s
  5. 5. ω = 7.05 rad/s
  6. 6. ω = 5.152 rad/s

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