Circular motion worksheet with answers

Free printable Circular motion 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
r = 100 m27 m/sF = ?

An 800 kg car drives around a flat curve of radius 100 m at a constant 27 m/s. Find the inward (centripetal) force Fc needed.

m = 800 kgv = 27 m/sr = 100 m
Fc = N
2.Easy
r = 0.4 mv200 rpm

A small object sits 40 cm from the axis of a disc that turns at a steady 200 revolutions per minute. Find its centripetal acceleration ac.

n = 200 rpmr = 0.4 m
ac = m/s²
3.Medium
r = 2.9 mn = ?

In a fairground rotor, riders stand against the wall of a vertical cylinder of radius 2.9 m. When it spins fast enough the floor drops away and friction holds them up. The coefficient of static friction is 0.8. Use g = 9.81 m/s². Find the smallest rotation rate n in revolutions per minute.

r = 2.9 mμs = 0.8g = 9.81 m/s²
n = rpm
4.Medium
r = 35 m11 m/s

A 1000 kg car drives over the top of a hump in the road at 11 m/s. The top of the hump is a circular arc of radius 35 m. Use g = 9.81 m/s². Find the normal force N of the road on the car at the top.

m = 1000 kgv = 11 m/sr = 35 mg = 9.81 m/s²
N = N
5.Hard
R = 6.5 mh = 31.2 m

A 1 kg cart is released from rest at a height of 31.2 m on a frictionless track and runs through a vertical loop of radius 6.5 m. Use g = 9.81 m/s². Find the normal force Ntop of the track on the cart at the top of the loop.

m = 1 kgh = 31.2 mR = 6.5 mg = 9.81 m/s²
Ntop = N
6.Hard
R = 0.5 mh = ?

A small cart is released from rest on a frictionless track and runs into a vertical loop of radius 0.5 m. From what minimum height hmin above the bottom of the loop must it start to stay on the track at the top of the loop?

R = 0.5 mv₀ = 0
hmin = m

Answer key

  1. 1. Fc = 5832 N
  2. 2. ac = 175.5 m/s²
  3. 3. n = 19.64 rpm
  4. 4. N = 6353 N
  5. 5. Ntop = 45.13 N
  6. 6. hmin = 1.25 m

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