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 290 kg and radius 0.45 m. It spins at 800 rpm. Find its kinetic energy E_k in kJ.

M = 290 kgR = 0.45 mn = 800 rpm

E_k = kJ

2.Easy

A flywheel is a uniform solid disc of mass 300 kg and radius 0.35 m. It spins at 700 rpm. Find its kinetic energy E_k in kJ.

M = 300 kgR = 0.35 mn = 700 rpm

E_k = kJ

3.Medium

A flywheel with a moment of inertia of 6.5 kg·m² spins at 2400 rpm. A brake applies a constant friction torque of 85 N·m. How many revolutions N does the flywheel make before it stops?

I = 6.5 kg·m²n = 2400 rpmT_b = 85 N·m

N = rev

4.Medium

A flywheel with a moment of inertia of 39.5 kg·m² spins at 400 rpm. A brake applies a constant friction torque of 155 N·m. How long t does it take to stop?

I = 39.5 kg·m²n = 400 rpmT_b = 155 N·m

t = s

5.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. Its radius is 0.15 m. Find its angular velocity ω after it has rolled 8.5 m along the slope.

θ = 35°s = 8.5 mI = m·r²g = 9.81 m/s²r = 0.15 m

ω = rad/s

6.Hard

A hollow sphere rolls without slipping down a slope inclined at 20° to the horizontal. Use g = 9.81 m/s². Find the smallest coefficient of static friction μ_s that prevents it from slipping.

θ = 20°I = (2/3)·m·r²g = 9.81 m/s²

μ_s =

Answer key

1. E_k = 103 kJ
2. E_k = 49.37 kJ
3. N = 384.4 rev
4. t = 10.67 s
5. ω = 46.11 rad/s
6. μ_s = 0.1456

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