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 100 kg and radius 0.8 m. It spins at 500 rpm. Find its kinetic energy E_k in kJ.

M = 100 kgR = 0.8 mn = 500 rpm

E_k = kJ

2.Easy

A flywheel is a uniform solid disc of mass 80 kg and radius 0.25 m. It spins at 1100 rpm. Find its kinetic energy E_k in kJ.

M = 80 kgR = 0.25 mn = 1100 rpm

E_k = kJ

3.Medium

A motor brings a flywheel with a moment of inertia of 34.5 kg·m² from rest up to 600 rpm in 8 s. Ignoring losses, find the average power P_avg it delivers, in kW.

I = 34.5 kg·m²n = 600 rpmt = 8 s

P_avg = kW

4.Medium

A shaft transmits 11.5 kW at 1500 rpm. Find the torque T in the shaft.

P = 11.5 kWn = 1500 rpm

T = N·m

5.Hard

A solid cylinder starts from rest and rolls without slipping down a slope inclined at 25° to the horizontal. Use g = 9.81 m/s². Find its speed v after it has rolled 1 m along the slope.

θ = 25°s = 1 mI = ½·m·r²g = 9.81 m/s²

v = m/s

6.Hard

A uniform slender rod of mass 1.5 kg and length 1.8 m hangs at rest from a frictionless pivot at its top end. A 45 g bullet moving horizontally at 480 m/s hits the rod 1.22 m below the pivot and stays embedded. Find the angular velocity ω of the rod just after the impact.

M = 1.5 kgL = 1.8 mm = 45 gv = 480 m/sd = 1.22 m

ω = rad/s

Answer key

1. E_k = 43.86 kJ
2. E_k = 16.59 kJ
3. P_avg = 8.513 kW
4. T = 73.21 N·m
5. v = 2.351 m/s
6. ω = 15.62 rad/s

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