Uniform circular motion – problems and solutions

1. An object moves in a circle with the constant angular speed of 10 rad/s. Determine (a) Angular speed after 10 seconds (b) Angular displacement after 10 seconds.

Known :

Angular speed (ω) =10 rad/s

Wanted :

(a) Angular speed (ω) after 10 seconds.

(b) Angle (θ) after 10 seconds

Solution :

(a) Angular speed (ω) after 10 seconds

Object in uniform circular motion so that angular speed is constant, 10 rad/s.

(b) Angular displacement (θ)

Constant angular speed 10 radians/second means the object around 10 radians each second. After 10 seconds, the object around 10 x 10 radians = 100 radians.

2. A particle moves in a circle with the constant speed of 10 m/s. Radius of circle = 1 meter. Determine (a) Particle’s speed after 5 seconds (b) Particle’s displacement after 5 seconds (c) Centripetal acceleration.

Known :

Radius of circle (r) = 1 meter

Particle’s speed (v) = 10 m/s

Solution :

(a) Particle’s speed after 5 seconds

The motion of object is in the uniform circular motion so that speed is constant, 10 m/s.

(b) Particle’s displacement after 5 seconds

10 meters/second means each 1 second, particle’s displacement = 10 meters. After 5 seconds, particle’s displacement = 5 x 10 meters = 50 meters.

(c) Centripetal acceleration (a_r)

a_r = v² / r = 10² / 1 = 100 / 1 = 100 m/s²

3. A ball attached to one end of a cord, is revolved in a circle with radius of 2 meters at the constant speed of 60 rpm. Determine (a) the magnitude of the angular speed after 2 seconds (b) the angular displacement after 1 minute.

Known :

Radius of circle (r) = 2 meters

Angular speed (ω) = 60 rpm = 60 revolutions / 1 minute

= 60 revolutions / 60 seconds = 1 revolution / second = 2π radians / second

= 2(3.14) radians / second= 6.28 radians / second

Solution :

(a) Angular speed (ω) after 2 seconds

The angular speed is constant so after 2 seconds, the angular speed (ω) = 6.28 radians / second

(b) Angular displacement (θ)

The angular speed = 1 revolution/second means each 1 second, ball experience 1 revolution. After 60 seconds, ball moves 60 revolutions.

The angular speed = 6.28 radians/second means each 1 second, the ball moves with the angle of 6.28 radians. After 60 seconds, the ball moves 376.8 radians.

4. A bike wheel rotates 120 revolutions in 60 seconds. What is the angular speed?

Solution :

(a) revolutions per minute (rpm)

120 revolutions / 60 seconds = 120 revolutions / 1 minute = 120 revolutions / minute = 120 rpm

(b) degrees per second (^o/s)

1 revolution = 360^o, 120 revolutions = 43200^o

120 revolutions / 60 seconds = (120)(360^o) / 60 seconds = 43200^o / 60 seconds = 720^o/second

(c) radians per second (rad/s)

1 revolution = 6.28 radians

120 revolutions / 60 seconds = (120)(6.28) radians / 60 seconds = 753.6 radians / 60 seconds = 12.56 radians/second.

[wpdm_package id=’432′]

[wpdm_package id=’439′]

1. Converting angle units sample problems with solutions
2. Angular displacement and linear displacement sample problems and solutions
3. Angular velocity and linear velocity sample problems with solutions
4. Angular acceleration and linear acceleration sample problems with solutions
5. Uniform circular motions sample problems with solutions
6. Centripetal acceleration sample problems with solutions
7. Nonuniform circular motions sample problems with solutions