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 50 kg with a radius of gyration of 0.35 m is accelerated uniformly from 800 rpm to 2400 rpm. The driving torque is a constant 57 N·m and friction can be ignored. How long t does this take?

m = 50 kgk = 0.35 mn₁ = 800 rpmn₂ = 2400 rpmT = 57 N·m

t = s

2.Easy

A flywheel of mass 120 kg with a radius of gyration of 0.55 m is accelerated uniformly from 300 rpm to 700 rpm. This takes 15 s. Ignoring friction, find the constant torque T needed.

m = 120 kgk = 0.55 mn₁ = 300 rpmn₂ = 700 rpmt = 15 s

T = N·m

3.Medium

A shaft transmits 30 kW at 1400 rpm. Find the torque T in the shaft.

P = 30 kWn = 1400 rpm

T = N·m

4.Medium

A flywheel with a moment of inertia of 16 kg·m² spins at 1700 rpm. A brake applies a constant friction torque of 200 N·m. How many revolutions N does the flywheel make before it stops?

I = 16 kg·m²n = 1700 rpmT_b = 200 N·m

N = rev

5.Hard

A thin hoop of mass 19.5 kg rolls without slipping at 4.5 m/s. Find its rotational kinetic energy E_rot.

m = 19.5 kgv = 4.5 m/sI = m·r²

E_rot = J

6.Hard

A solid cylinder starts from rest and rolls without slipping down a slope inclined at 30° to the horizontal. Use g = 9.81 m/s². Its radius is 0.1 m. Find its angular velocity ω after it has rolled 8 m along the slope.

θ = 30°s = 8 mI = ½·m·r²g = 9.81 m/s²r = 0.1 m

ω = rad/s

Answer key

1. t = 18 s
2. T = 101.4 N·m
3. T = 204.6 N·m
4. N = 201.8 rev
5. E_rot = 197.4 J
6. ω = 72.33 rad/s

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