The net inward force required to keep an object moving along a circular path, directed toward the centre of the circle, equal to mv2/r where m is the object's mass, v its speed, and r the radius of the circle.
The force that pulls you toward the center when you go around a curve.
Showing a random 20 of 50 problems.
Example 1
medium
A 0.5 kg ball on a 1.2 m string is swung in a horizontal circle at 4 m/s. What is the centripetal force?F_c ⊥ v. F_c = mv²/r = 0.5 × 16 / 1.2 ≈ 6.67 N toward the center.
Example 2
easy
In which direction does the centripetal force on an object in circular motion point?
Example 3
medium
A satellite needs centripetal force from gravity. A 500 kg satellite orbits at 7000 m/s with radius... given gravity provides 2500 N, find the orbital radius.
Example 4
easy
A car of mass 1000 kg rounds a curve of radius 50 m at 10 m/s. Find the centripetal force.
Example 5
easy
If the radius of an object's circular path is doubled while its speed stays the same, by what factor does the centripetal force change?
Example 6
challenge
A satellite of mass m orbits Earth at radius r where gravity gives acceleration g(r). Show that orbital speed is v=g(r)r and compute it for r=6.6×106 m with g(r)=9.2 m/s2.
Example 7
medium
A car on a banked curve relies only on the horizontal component of the normal force. The banking angle is 20∘ and the radius is 40 m. Find the design speed. Use g=10 m/s2.N sin 20° = F_c; N cos 20° = mg. Design speed ≈ 12.1 m/s.
Example 8
challenge
A 2 kg ball swings in a vertical circle (radius 1 m) at 5 m/s at the bottom (g=10 m/s2). Find the tension at the bottom.T − mg = mv²/r = 50 N. T = 70 N supports both weight and centripetal need.
Example 9
easy
Is centripetal force a new kind of force, or the net of existing forces?
Example 10
easy
Centrifugal force is a ___ force that appears in a rotating reference frame.
Example 11
medium
A 0.5 kg ball swings in a vertical circle of radius 0.8 m at 5 m/s at the top of the loop. Find the tension in the string at the top. Use g=10 m/s2.T + mg = mv²/r = 15.6 N. So T = 15.6 − 5 = 10.6 N.
Example 12
medium
A 0.3 kg ball at the end of a 1 m string moves in a horizontal circle making 1.5 rev/s. Find the centripetal force.
Example 13
challenge
A coin sits 0.1 m from the center of a turntable. The max static friction gives a=4 m/s2. Find the maximum angular speed before it slips.
Example 14
easy
A 1.5 kg ball moves in a circle of radius 0.5 m with centripetal acceleration 20 m/s2. Find the centripetal force.
Example 15
medium
A 0.3 kg mass on a 0.4 m string is whirled horizontally; the string breaks at 48 N tension. Find the maximum speed.T_max = mv²/r = 48 N → v = √(T_max r/m) = √64 = 8 m/s.
Example 16
medium
A conical pendulum: a 1 kg ball swings so the string makes 30∘ with vertical (g=10 m/s2). Find the string tension.Tension T decomposes: T cos 30° balances weight; T sin 30° is the centripetal force.
Example 17
hard
A coin sits on a turntable 0.15 m from the axis. The coefficient of static friction is 0.4. Find the maximum rotation rate in rev/s before the coin slips. Use g=10 m/s2.
Example 18
medium
A car rounds a flat curve of radius 40 m. The max friction force is 4000 N and the car is 1000 kg. Find the maximum safe speed.f_max = mv²/r → v_max = √(f_max r/m) = √160 ≈ 12.6 m/s.
Example 19
hard
A 0.2 kg ball swings on a 0.5 m string in a vertical circle at constant speed 4 m/s. Find the tension when the string is horizontal. Use g=10 m/s2.At the horizontal position: tension alone equals F_c = mv²/r = 6.4 N. Weight is tangential.
Example 20
medium
An astronaut in a centrifuge sits 5 m from the rotation axis. To feel 3g of centripetal acceleration, what angular speed is needed? Use g=10 m/s2.