Motion of an object along a circular path where the speed may be constant but the velocity is continuously changing direction, requiring a centripetal acceleration.
A car on a circular track at constant speed is still accelerating—toward the center.
Showing a random 20 of 50 problems.
Example 1
medium
A car drives at 20 m/s around a curve. To halve its centripetal acceleration, by what factor should the radius change?
Example 2
easy
An object speeds around a circle of radius 5 m at 10 m/s. Centripetal acceleration?
Example 3
medium
A point at radius r and one at radius 2r on the same rigid wheel. Compare their speeds.Same angular speed: outer point at r
Example 4
challenge
A roller-coaster loop of radius 8 m. What minimum speed at the top guarantees riders stay seated (use g=9.8)?Roller-coaster loop r
Example 5
medium
A point moves in a circle of radius 4 m, completing a revolution in 8 s. Find its speed.
Example 6
easy
An object completes a circle of radius 3 m. What distance does one revolution cover?
Example 7
medium
A point on the rim of a bicycle wheel (r=0.35 m) moves at 5 m/s. What is the period of rotation and the centripetal acceleration?
Example 8
medium
A wheel turns through one revolution in 0.5 s, radius 0.4 m. Find the tip speed.
Example 9
medium
An object needs centripetal acceleration 18 m/s2 on a radius 2 m. Find its speed.
Example 10
challenge
A coin sits 0.1 m from the center of a turntable. If max static friction gives a=2 m/s2, find the maximum frequency before it slips.
Example 11
easy
At constant speed on a circle, is the velocity changing?
Example 12
easy
An object moves at constant v=8 m/s on a circle of radius r=4 m. Find the centripetal acceleration.
Example 13
easy
Period T=4 s for one revolution. What is the frequency?
Example 14
easy
A wheel spins so a point goes around in 2 s. How many revolutions in 10 s?
Example 15
hard
A ball on a 0.8 m string is swung in a vertical circle. What minimum speed must it have at the top of the circle so the string remains taut? Use g=9.8 m/s2.
Example 16
medium
A car on a curve of radius 40 m has ac=4 m/s2. Find its speed.
Example 17
challenge
Earth orbits the Sun at radius 1.5×1011 m with period T=3.16×107 s. Find the centripetal acceleration.
Example 18
easy
A car rounds a circular track at constant speed. Is it accelerating?
Example 19
medium
A satellite orbits at constant v=7000 m/s at radius 7×106 m. Find the centripetal acceleration.
Example 20
medium
A satellite orbits Earth at a radius of 6.8×106 m with a period of 5400 s. What is its orbital speed and centripetal acceleration?