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 8.5 kg and length 1.6 m rotates about an axis O perpendicular to the rod, 0.8 m from its centre G. Find its mass moment of inertia I_O about that axis.

m = 8.5 kgL = 1.6 md = 0.8 m

I_O = kg·m²

2.Easy

A flywheel of mass 150 kg with a radius of gyration of 0.25 m is accelerated uniformly from 500 rpm to 2200 rpm. This takes 11 s. Ignoring friction, find the constant torque T needed.

m = 150 kgk = 0.25 mn₁ = 500 rpmn₂ = 2200 rpmt = 11 s

T = N·m

3.Medium

A motor delivers a torque of 700 N·m at 2800 rpm. Find its power output P in kW.

T = 700 N·mn = 2800 rpm

P = kW

4.Medium

An 11 kg block hangs from a light cord wrapped around a pulley, a uniform solid disc of mass 17.5 kg and radius 0.2 m that turns on a frictionless horizontal axle. The block is released from rest. Use g = 9.81 m/s². Find the speed v of the block after it has fallen 2 m.

m = 11 kgM = 17.5 kgR = 0.2 mg = 9.81 m/s²h = 2 m

v = m/s

5.Hard

A hollow sphere of mass 5.5 kg rolls without slipping at 8.5 m/s. What percentage p of its total kinetic energy is rotational?

m = 5.5 kgv = 8.5 m/sI = (2/3)·m·r²

p = %

6.Hard

A hollow sphere starts from rest and rolls without slipping down a slope inclined at 30° to the horizontal. Use g = 9.81 m/s². Find its speed v after it has rolled 8.5 m along the slope.

θ = 30°s = 8.5 mI = (2/3)·m·r²g = 9.81 m/s²

v = m/s

Answer key

1. I_O = 7.253 kg·m²
2. T = 151.7 N·m
3. P = 205.3 kW
4. v = 4.675 m/s
5. p = 40 %
6. v = 7.073 m/s

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