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 = 0.35 m0 → 1700 rpm50 kg

A flywheel of mass 50 kg with a radius of gyration of 0.35 m is accelerated uniformly from rest to 1700 rpm. This takes 30 s. Ignoring friction, find the constant torque T needed.

m = 50 kgk = 0.35 mn1 = 0 rpmn2 = 1700 rpmt = 30 s
T = N·m
2.Easy
k = 0.15 m0 → 900 rpm10 kg

A flywheel of mass 10 kg with a radius of gyration of 0.15 m is accelerated uniformly from rest to 900 rpm. The driving torque is a constant 0.73 N·m and friction can be ignored. How long t does this take?

m = 10 kgk = 0.15 mn1 = 0 rpmn2 = 900 rpmT = 0.73 N·m
t = s
3.Medium
v = ?L = 1.8 mm = 3 kg

A uniform slender rod of mass 3 kg and length 1.8 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 = 1.8 mg = 9.81 m/s²
v = m/s
4.Medium
L = 2.7 mm = 6 kgα

A uniform slender rod of mass 6 kg and length 2.7 m is pinned at one end and held horizontal. It is released from rest. Use g = 9.81 m/s². Find the vertical force R that the pin exerts on the rod just after release.

m = 6 kgL = 2.7 mg = 9.81 m/s²
R = N
5.Hard
θ = 25°a

A thin hoop rolls without slipping down a slope inclined at 25° to the horizontal. Use g = 9.81 m/s². Find the acceleration a of its centre.

θ = 25°I = m·r²g = 9.81 m/s²
a = m/s²
6.Hard
0.75 m0.3 mn1​ = 25 rpm

A person stands on a frictionless turntable and holds a 5.5 kg dumbbell in each hand, 0.75 m from the axis. The person and turntable alone have a moment of inertia of 4 kg·m² about the axis. They turn at 25 rpm, then pull the dumbbells in to 0.3 m from the axis. Treat the dumbbells as point masses. Find the new speed n2 in rpm.

I0 = 4 kg·m²m = 2 × 5.5 kgr1 = 0.75 mr2 = 0.3 mn1 = 25 rpm
n2 = rpm

Answer key

  1. 1. T = 36.35 N·m
  2. 2. t = 29.05 s
  3. 3. v = 7.278 m/s
  4. 4. R = 14.72 N
  5. 5. a = 2.073 m/s²
  6. 6. n2 = 51.04 rpm

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