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 210 kg and radius 0.3 m. It spins at 3000 rpm. Find its kinetic energy E_k in kJ.

M = 210 kgR = 0.3 mn = 3000 rpm

E_k = kJ

2.Easy

A flywheel is a uniform solid disc of mass 250 kg and radius 0.45 m. It spins at 2600 rpm. Find its kinetic energy E_k in kJ.

M = 250 kgR = 0.45 mn = 2600 rpm

E_k = kJ

3.Medium

A uniform slender rod of mass 5 kg and length 1.4 m is pinned at one end and held horizontal. It is released from rest. Use g = 9.81 m/s². Find the vertical force R that the pin exerts on the rod just after release.

m = 5 kgL = 1.4 mg = 9.81 m/s²

R = N

4.Medium

A motor delivers a torque of 1690 N·m at 1300 rpm. Find its power output P in kW.

T = 1690 N·mn = 1300 rpm

P = kW

5.Hard

A solid sphere starts from rest and rolls without slipping down a slope inclined at 10° to the horizontal. Use g = 9.81 m/s². Its radius is 0.35 m. Find its angular velocity ω after it has rolled 9.5 m along the slope.

θ = 10°s = 9.5 mI = (2/5)·m·r²g = 9.81 m/s²r = 0.35 m

ω = rad/s

6.Hard

A solid sphere rolls without slipping down a slope inclined at 35° to the horizontal. Use g = 9.81 m/s². It starts from rest. How long t does it take to roll 1 m down the slope?

θ = 35°I = (2/5)·m·r²g = 9.81 m/s²s = 1 m

t = s

Answer key

1. E_k = 466.3 kJ
2. E_k = 938.2 kJ
3. R = 12.26 N
4. P = 230.1 kW
5. ω = 13.74 rad/s
6. t = 0.7054 s

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