# Uniform motion in a horizontal circle – problems and solutions

1. A 0.2-kg ball, attached to the end of a horizontal cord, is revolved in a circle of radius 1 meter and ball’s maximum speed is 10 rpm. What is the magnitude of the centripetal acceleration and the magnitude of the tension force?

__Known :__

Mass (m) = 0.2 kg

Radius (r) = 1 m

Angular velocity (ω) = 10 rev/min = 10 rev/60 s = 0.17 rev/s = (0.17)(6.28 rad)/s = 1 rad/s

Velocity (v) = r ω = (1 m)(1 rad/s) = 1 m/s

__Wanted :__ a_{s} dan ΣF

__Solution :__

(a) The magnitude of the centripetal acceleration

(b) The magnitude of the tension force

ΣF = m a

T = m a_{s}

T = (0.2 kg)(1 m/s^{2})

T = 0.2 kg m/s^{2}

T = 0.2 N

2. A 1-kg ball at the end of a string is revolving uniformly in a horizontal circle of radius 1 m. The cord will break when the tension in it exceeds 100 N. What is the maximum speed the ball can have?

__Known :__

Mass (m) = 1 kg

Radius (r) = 1 meter

Tension force (T) = centripetal force (ΣF) = 100 N

__Wanted:__ v maximum

__Solution :__

- Mass and weight
- Normal force
- Newton’s second law of motion
- Friction force
- Motion on a horizontal surface without friction force
- The motion of two bodies with the same acceleration on the rough horizontal surface with a friction force
- Motion on an inclined plane without friction force
- Motion on the rough inclined plane with the friction force
- Motion in an elevator
- The motion of bodies connected by cord and pulley
- Two bodies with the same magnitude of accelerations
- Rounding a flat curve – dynamics of circular motion
- Rounding a banked curve – dynamics of circular motion
- Uniform motion in a horizontal circle
- Centripetal force in uniform circular motion