A 40 kg child sits at the edge of a merry-go-round of radius 3 m, turning once every 6 s at a steady speed. Three questions hide in that one sentence: how fast the child moves, how big a force must point at the center to hold her there, and which real force is doing it.
You already have every tool. The equation v = 2πr/T gives the speed of steady circular motion. The equation F = mv²/r gives the required net inward force. And the supplier question names the real force. A full analysis runs them in that order.
Step 1: find the speed. The radius and the period are given, so v = 2πr/T does it.
Step 2: find the required force. With the speed known, F = mv²/r gives the net inward force the circle requires.
Step 3: name the supplier. The child turns on a flat platform, with nothing tied to her and nothing walling her in: friction between her and the platform supplies her centripetal force.
Every quantity keeps its unit through the working: r in m, T in s, v in m/s, m in kg, F in N.
A 40 kg child sits 3 m from the center of a merry-go-round turning once every 6 s at a steady speed. Find her speed, find the required centripetal force, and name the force that supplies it. Use π ≈ 3.14.
Write down the values:
m = 40 kg, r = 3 m, T = 6 s, v = ?, F = ?
Write down the first equation:
v = 2πr/T
Substitute in the values, and calculate:
v = 2 × 3.14 × 3 ÷ 6
2 × 3.14 = 6.28
6.28 × 3 = 18.84
18.84 ÷ 6 = 3.14
v ≈ 3.14 m/s
Write down the second equation:
F = mv²/r
Substitute in the values, and calculate:
F = 40 × 3.14² ÷ 3
3.14 × 3.14 = 9.86
40 × 9.86 = 394.4
394.4 ÷ 3 = 131.47
F ≈ 130 N
Name the supplier: the child turns on a flat platform, so friction between her and the platform supplies the force.
The child moves at about 3.14 m/s. Her circle requires about 130 N toward the center, and friction between her and the platform supplies it.
A drone flies a circle of radius 5 m at a steady speed, completing one lap every 4 s. Enter the drone's speed in m/s. Use π ≈ 3.14. Answers within 2% are accepted.
A 30 kg crate rides a rotating platform, 6 m from the center, moving at a steady 4 m/s. Enter the centripetal force the crate's circle requires, in N.
A 0.5 kg puck on a cord circles a center peg on an ice rink, at radius 2 m, once every 2 s, at a steady speed. Find its speed, find the required centripetal force, and name the supplier. Use π ≈ 3.14.
Write down the values:
m = 0.5 kg, r = 2 m, T = 2 s, v = ?, F = ?
Write down the first equation:
v = 2πr/T
Substitute in the values, and calculate:
v = 2 × 3.14 × 2 ÷ 2
2 × 3.14 = 6.28
6.28 × 2 = 12.56
12.56 ÷ 2 = 6.28
v ≈ 6.28 m/s
Write down the second equation:
F = mv²/r
Substitute in the values, and calculate:
F = 0.5 × 6.28² ÷ 2
6.28 × 6.28 = 39.44
0.5 × 39.44 = 19.72
19.72 ÷ 2 = 9.86
F ≈ 9.9 N
Name the supplier: the cord runs from the puck to the peg at the center, so its tension supplies the force.
The puck moves at about 6.28 m/s. Its circle requires about 9.9 N toward the center, and the cord's tension supplies it.
A kayaker holds a towline anchored to a buoy and circles the buoy at a steady speed. After you compute the required centripetal force, which real force supplies it?
A 50 kg runner rounds a circular track lane of radius 10 m at a steady speed, completing one lap every 20 s. Enter the centripetal force her circle requires, in N. Use π ≈ 3.14. Answers within 2% are accepted.
A 1.2 kg radio-controlled car circles a center stake on a taut tether of radius 4 m, at a steady speed, once every 4 s. Enter the centripetal force its circle requires, in N. Use π ≈ 3.14. Answers within 2% are accepted.
A delivery robot drives a circle on a flat plaza at a steady speed. In the full analysis of its motion, which real force supplies the required centripetal force?