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 20 kg with a radius of gyration of 0.45 m is accelerated uniformly from rest to 1900 rpm. This takes 15 s. Ignoring friction, find the constant torque T needed.

m = 20 kgk = 0.45 mn₁ = 0 rpmn₂ = 1900 rpmt = 15 s

T = N·m

2.Easy

A flywheel is a uniform solid disc of mass 40 kg and radius 0.4 m. It spins at 2600 rpm. Find its kinetic energy E_k in kJ.

M = 40 kgR = 0.4 mn = 2600 rpm

E_k = kJ

3.Medium

A flywheel with a moment of inertia of 19.5 kg·m² spins at 300 rpm. A brake applies a constant friction torque of 95 N·m. How many revolutions N does the flywheel make before it stops?

I = 19.5 kg·m²n = 300 rpmT_b = 95 N·m

N = rev

4.Medium

A flywheel with a moment of inertia of 39 kg·m² spins at 1400 rpm. A brake applies a constant friction torque of 110 N·m. How many revolutions N does the flywheel make before it stops?

I = 39 kg·m²n = 1400 rpmT_b = 110 N·m

N = rev

5.Hard

A solid cylinder of mass 16 kg rolls without slipping at 3 m/s. Find its total kinetic energy E_k.

m = 16 kgv = 3 m/sI = ½·m·r²

E_k = J

6.Hard

A hollow sphere starts from rest and rolls without slipping down a slope inclined at 15° to the horizontal. Use g = 9.81 m/s². Find its speed v after it has rolled 4 m along the slope.

θ = 15°s = 4 mI = (2/3)·m·r²g = 9.81 m/s²

v = m/s

Answer key

1. T = 53.72 N·m
2. E_k = 118.6 kJ
3. N = 16.12 rev
4. N = 606.4 rev
5. E_k = 108 J
6. v = 3.491 m/s

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