## Angular velocity and linear velocity – problems and solutions

1. A ball at the end of a string is revolving uniformly in a horizontal circle of radius 2 meters at constant angular speed 10 rad/s. Determine the magnitude of the linear velocity of a point located : (a) 0.5 meters from the center (b) 1 meter from the center (c) 2 meters from the …

## Angular displacement and linear displacement – problems and solutions

Converting angle units (degree, radian, revolution) 1. ¼ rev = ….. o (degree) ? Solution 1 rev = 360o ½ rev = 180o ¼ rev = 90o 2. ½ rev = …….. rad ? Solution 1 rev = 2π rad = 2(3.14) rad = 6.28 rad ½ rev = pi rad = 3.14 rad 3. …

## Nonuniform circular motion – problems and solutions

1. A wheel 1 meter in radius accelerates uniformly at 2 rad/s2. Determine the angular acceleration and the angular speed of the wheel, 2 seconds later. Known : Radius (r) = 1 meter Angular acceleration (α) = 2 rad/s2 Wanted: angular acceleration and angular speed after 2 seconds. Solution : (a) Angular acceleration in 2 …

## 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 …

## Centripetal force in uniform circular motion – problems and solutions

1. A 0.1-kg ball, attached to the end of a horizontal cord, is revolved in a circle of radius 50 cm and ball’s angular speed is 4 rad s-1. What is the magnitude of the centripetal force? Known : Mass (m) = 100 gram = 100/1000 kg = 1/10 kg = 0.1 kg Angular speed …

## 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 …

## Rounding a banked curve – dynamics of circular motion problems and solutions

1. A car rounding a banked curve. What is an angle for the road which has a curve of radius 60 meters with a design speed of 20 m/ s? Assume there is no friction between car and road. Solution N = normal force N sin θ = horizontal component of the normal force N …

## Rounding a flat curve – dynamics of circular motion problems and solutions

1. A 2000-kg car rounds a curve on a flat road of radius 150 m. The coefficient of static friction is 0.5. Determine the maximum speed so the car follows the curve and not skid. Acceleration due to gravity = 10 m/s2. Known : Mass (m) = 2000 kg Radius (r) = 150 meters Coefficient …

## Two bodies with the same magnitude of acceleration – Application of Newton’s law of motion problems and solutions

1. Two masses m1 = 2 kg and m2 = 5 kg are on inclined plane and are connected together by a string as shown in the figure. The coefficient of the kinetic friction between m1 and incline is 0.2 and the coefficient of the kinetic friction between m2 and incline is 0.1. (a) Determine …

## Equilibrium of the bodies on a inclined plane – application of the Newton’s first law problems and solutions

1. A 2-kg block lies on a rough inclined plane at an angle 37o to the horizontal. Determine the magnitude of the external force exerted on the block, so the block is not slides down the plane. (sin 37o = 0.6, cos 37o = 0.8, g = 10 m.s-2, µk = 0.2) Known : Mass …