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 = 0.15 m0 → 1300 rpm60 kg

A flywheel of mass 60 kg with a radius of gyration of 0.15 m is accelerated uniformly from rest to 1300 rpm. The driving torque is a constant 17 N·m and friction can be ignored. How long t does this take?

m = 60 kgk = 0.15 mn1 = 0 rpmn2 = 1300 rpmT = 17 N·m
t = s
2.Easy
k = 0.25 mn = 2200 rpm30 kg

A flywheel of mass 30 kg has a radius of gyration of 0.25 m about its axis. It spins at 2200 rpm. Find its kinetic energy Ek in kJ.

M = 30 kgk = 0.25 mn = 2200 rpm
Ek = kJ
3.Medium
7.5 kgaαM = 4.5 kgR = 0.35 m

A 7.5 kg block hangs from a light cord wrapped around a pulley, a uniform solid disc of mass 4.5 kg and radius 0.35 m that turns on a frictionless horizontal axle. The block is released from rest. Use g = 9.81 m/s². Find the acceleration a of the block.

m = 7.5 kgM = 4.5 kgR = 0.35 mg = 9.81 m/s²
a = m/s²
4.Medium
n = 400 rpmT = 510 N·m

A motor delivers a torque of 510 N·m at 400 rpm. Find its power output P in kW.

T = 510 N·mn = 400 rpm
P = kW
5.Hard
disc: 27 kgring: 5 kgn1​ = 650 rpm

A uniform solid disc (mass 27 kg, radius 0.35 m) spins freely at 650 rpm about a vertical frictionless shaft. A thin ring of mass 5 kg and the same radius is dropped onto it from rest, centred on the shaft, and the two quickly spin together. How much kinetic energy ΔE is lost in the process?

Mdisc = 27 kgMring = 5 kgR = 0.35 mn1 = 650 rpm
ΔE = J
6.Hard
9.5 m/sω

A hollow sphere of mass 15.5 kg rolls without slipping at 9.5 m/s. Find its rotational kinetic energy Erot.

m = 15.5 kgv = 9.5 m/sI = (2/3)·m·r²
Erot = J

Answer key

  1. 1. t = 10.81 s
  2. 2. Ek = 49.76 kJ
  3. 3. a = 7.546 m/s²
  4. 4. P = 21.36 kW
  5. 5. ΔE = 1035 J
  6. 6. Erot = 466.3 J

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