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 10 kg with a radius of gyration of 0.5 m is accelerated uniformly from 900 rpm to 1400 rpm. This takes 25 s. Ignoring friction, find the constant torque T needed.

m = 10 kgk = 0.5 mn₁ = 900 rpmn₂ = 1400 rpmt = 25 s

T = N·m

2.Easy

A flywheel of mass 90 kg with a radius of gyration of 0.25 m is accelerated uniformly from 800 rpm to 1300 rpm. The driving torque is a constant 14 N·m and friction can be ignored. How long t does this take?

m = 90 kgk = 0.25 mn₁ = 800 rpmn₂ = 1300 rpmT = 14 N·m

t = s

3.Medium

A motor brings a flywheel with a moment of inertia of 33 kg·m² from rest up to 2200 rpm in 9 s. Ignoring losses, find the average power P_avg it delivers, in kW.

I = 33 kg·m²n = 2200 rpmt = 9 s

P_avg = kW

4.Medium

A motor brings a flywheel with a moment of inertia of 25.5 kg·m² from rest up to 900 rpm in 10 s. Ignoring losses, find the average power P_avg it delivers, in kW.

I = 25.5 kg·m²n = 900 rpmt = 10 s

P_avg = kW

5.Hard

A hollow sphere of mass 3.5 kg rolls without slipping at 8 m/s. Find its total kinetic energy E_k.

m = 3.5 kgv = 8 m/sI = (2/3)·m·r²

E_k = J

6.Hard

A solid cylinder starts from rest and rolls without slipping down a slope inclined at 35° to the horizontal. Use g = 9.81 m/s². Find its speed v after it has rolled 2.5 m along the slope.

θ = 35°s = 2.5 mI = ½·m·r²g = 9.81 m/s²

v = m/s

Answer key

1. T = 5.236 N·m
2. t = 21.04 s
3. P_avg = 97.31 kW
4. P_avg = 11.33 kW
5. E_k = 186.7 J
6. v = 4.331 m/s

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