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 is a uniform solid disc of mass 80 kg and radius 0.6 m. It spins at 2400 rpm. Find its kinetic energy E_k in kJ.

M = 80 kgR = 0.6 mn = 2400 rpm

E_k = kJ

2.Easy

A flywheel is a uniform solid disc of mass 300 kg and radius 0.55 m. It spins at 1400 rpm. Find its kinetic energy E_k in kJ.

M = 300 kgR = 0.55 mn = 1400 rpm

E_k = kJ

3.Medium

A flywheel with a moment of inertia of 12.5 kg·m² spins at 1100 rpm. A brake applies a constant friction torque of 155 N·m. How many revolutions N does the flywheel make before it stops?

I = 12.5 kg·m²n = 1100 rpmT_b = 155 N·m

N = rev

4.Medium

A uniform slender rod of mass 18 kg and length 0.7 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 = 18 kgL = 0.7 mg = 9.81 m/s²

a_tip = m/s²

5.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. Its radius is 0.3 m. Find its angular velocity ω after it has rolled 8 m along the slope.

θ = 15°s = 8 mI = (2/3)·m·r²g = 9.81 m/s²r = 0.3 m

ω = rad/s

6.Hard

A solid cylinder 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 3.5 m along the slope.

θ = 15°s = 3.5 mI = ½·m·r²g = 9.81 m/s²

v = m/s

Answer key

1. E_k = 454.8 kJ
2. E_k = 487.6 kJ
3. N = 85.16 rev
4. a_tip = 14.71 m/s²
5. ω = 16.46 rad/s
6. v = 3.442 m/s

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