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 40 kg with a radius of gyration of 0.4 m is accelerated uniformly from rest to 200 rpm. The driving torque is a constant 34 N·m and friction can be ignored. How long t does this take?

m = 40 kgk = 0.4 mn₁ = 0 rpmn₂ = 200 rpmT = 34 N·m

t = s

2.Easy

A flywheel of mass 300 kg has a radius of gyration of 0.4 m about its axis. It spins at 1500 rpm. Find its kinetic energy E_k in kJ.

M = 300 kgk = 0.4 mn = 1500 rpm

E_k = kJ

3.Medium

A flywheel with a moment of inertia of 24 kg·m² spins at 1100 rpm. A brake applies a constant friction torque of 90 N·m. How many revolutions N does the flywheel make before it stops?

I = 24 kg·m²n = 1100 rpmT_b = 90 N·m

N = rev

4.Medium

A flywheel with a moment of inertia of 3.5 kg·m² spins at 1200 rpm. A brake applies a constant friction torque of 55 N·m. How many revolutions N does the flywheel make before it stops?

I = 3.5 kg·m²n = 1200 rpmT_b = 55 N·m

N = rev

5.Hard

A hollow sphere of mass 4.5 kg rolls without slipping at 10 m/s. What percentage p of its total kinetic energy is rotational?

m = 4.5 kgv = 10 m/sI = (2/3)·m·r²

p = %

6.Hard

A thin hoop 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 9 m along the slope.

θ = 35°s = 9 mI = m·r²g = 9.81 m/s²

v = m/s

Answer key

1. t = 3.942 s
2. E_k = 592.2 kJ
3. N = 281.6 rev
4. N = 79.97 rev
5. p = 40 %
6. v = 7.116 m/s

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