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

A flywheel of mass 80 kg has a radius of gyration of 0.35 m about its axis. It spins at 2000 rpm. Find its kinetic energy E_k in kJ.

M = 80 kgk = 0.35 mn = 2000 rpm

E_k = kJ

2.Easy

A flywheel is a uniform solid disc of mass 80 kg and radius 0.3 m. It spins at 2400 rpm. Find its kinetic energy E_k in kJ.

M = 80 kgR = 0.3 mn = 2400 rpm

E_k = kJ

3.Medium

A flywheel with a moment of inertia of 34.5 kg·m² spins at 700 rpm. A brake applies a constant friction torque of 125 N·m. How long t does it take to stop?

I = 34.5 kg·m²n = 700 rpmT_b = 125 N·m

t = s

4.Medium

A flywheel with a moment of inertia of 5.5 kg·m² spins at 1300 rpm. A brake applies a constant friction torque of 70 N·m. How long t does it take to stop?

I = 5.5 kg·m²n = 1300 rpmT_b = 70 N·m

t = s

5.Hard

A uniform slender rod of mass 10 kg and length 0.7 m hangs at rest from a frictionless pivot at its top end. A 40 g bullet moving horizontally at 400 m/s hits the rod 0.63 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 = 10 kgL = 0.7 mm = 40 gv = 400 m/sd = 0.63 mg = 9.81 m/s²

φ = °

6.Hard

A solid cylinder of mass 5 kg rolls without slipping at 6.5 m/s. What percentage p of its total kinetic energy is rotational?

m = 5 kgv = 6.5 m/sI = ½·m·r²

p = %

Answer key

1. E_k = 214.9 kJ
2. E_k = 113.7 kJ
3. t = 20.23 s
4. t = 10.7 s
5. φ = 83.73 °
6. p = 33.33 %

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