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.

New worksheet Practise online with hints

For teachers: free to print, copy and use in class. Every new worksheet has new values and its own answer key. A link to ExamProblems on your course page is appreciated.

Name: ____________________ Date: ____________

1.Easy

A uniform slender rod of mass 1.5 kg and length 2.3 m rotates about an axis O perpendicular to the rod, 0.4 m from its centre G. Find its mass moment of inertia I_O about that axis.

m = 1.5 kgL = 2.3 md = 0.4 m

I_O = kg·m²

2.Easy

A flywheel of mass 20 kg with a radius of gyration of 0.45 m is accelerated uniformly from 300 rpm to 2000 rpm. The driving torque is a constant 40 N·m and friction can be ignored. How long t does this take?

m = 20 kgk = 0.45 mn₁ = 300 rpmn₂ = 2000 rpmT = 40 N·m

t = s

3.Medium

A flywheel with a moment of inertia of 19.5 kg·m² spins at 1000 rpm. A brake applies a constant friction torque of 195 N·m. How long t does it take to stop?

I = 19.5 kg·m²n = 1000 rpmT_b = 195 N·m

t = s

4.Medium

A uniform slender rod of mass 1 kg and length 1.8 m is pinned at one end and held horizontal. It is released from rest. Use g = 9.81 m/s². Find the acceleration a_tip of the free end just after release.

m = 1 kgL = 1.8 mg = 9.81 m/s²

a_tip = m/s²

5.Hard

A solid sphere rolls without slipping down a slope inclined at 20° to the horizontal. Use g = 9.81 m/s². It starts from rest. How long t does it take to roll 4 m down the slope?

θ = 20°I = (2/5)·m·r²g = 9.81 m/s²s = 4 m

t = s

6.Hard

A hollow sphere of mass 19.5 kg rolls without slipping at 1.5 m/s. What percentage p of its total kinetic energy is rotational?

m = 19.5 kgv = 1.5 m/sI = (2/3)·m·r²

p = %

Answer key

1. I_O = 0.9012 kg·m²
2. t = 18.02 s
3. t = 10.47 s
4. a_tip = 14.71 m/s²
5. t = 1.827 s
6. p = 40 %

Full step-by-step solutions: practise this topic on examproblems.com.