Constant Angular Acceleration

The particle began to move from rest along a circle with a constant angular acceleration. After five cycles (n = 5), its angular velocity reached the value ω = 12 rad/s.
Calculate the magnitude of the angular acceleration ε of this motion and the time interval required for the first 5 cycles.

Correct result:

ε =  2.2918 rad/s²
t =  5.236 s

Solution:

$$\begin{gathered} \omega =12\text{ rad/s } \\ n=5 \\ \alpha =n\cdot 2\pi =5\cdot 2\cdot 3.1416\doteq 31.4159\text{ rad } \\ \alpha ={\displaystyle \frac{1}{2}}\cdot \epsilon \cdot t^2 \\ \epsilon =\omega \mathrm{/}t \\ \alpha ={\displaystyle \frac{1}{2}}\cdot \omega \mathrm{/}t\cdot t^2 \\ \alpha ={\displaystyle \frac{1}{2}}\cdot \omega \cdot t \\ t=2\cdot \alpha \mathrm{/}\omega =2\cdot 31.4159\mathrm{/}12\doteq 5.236\text{ s } \\ \epsilon =\omega \mathrm{/}t=12\mathrm{/}5.236=2.2918{\text{rad/s}}^2 \end{gathered}$$

Try another example

Showing 0 comments:

Related math problems and questions:

• Circular motion
  Mass point moves moves uniformly in a circle with radius r = 3.4 m angular velocity ω = 3.6 rad/s. Calculate the period, frequency, and the centripetal acceleration of this movement.
• Acceleration
  The car accelerates at rate 0.5m/s². How long travels 400 meters and what will be its speed?
• Brakes
  The braking efficiency of a passenger car is required to stop at 12.5 m at an initial speed of 40 km/h. What is the acceleration braking by brakes?
• Rotaty motion
  What is the minimum speed and frequency that we need to rotate with water can in a vertical plane along a circle with a radius of 70 cm to prevent water from spilling?
• Propeller
  The aircraft propeller rotates at an angular speed of 200 rad/s. A) What is the speed at the tip of the propeller if its distance from the axis of rotation is 1.5 m? B) What path does the aircraft travel during one revolution of the propeller at a speed o
• Acceleration 2
  if a car traveling at a velocity of 80 m/s/south accelerated to a velocity of 100 m/s east in 5 seconds, what is the cars acceleration? using Pythagorean theorem
• Driver
  The driver of the car at a speed of 100 km/h faced the obstacle and began to brake with a slowing of 5 m/s². What is the path to stopping the car when the driver has registered the obstacle with a delay of 0.7 s?
• Paratrooper
  After the parachute is opened, the paratrooper drops to the ground at a constant speed of 2 m/s, with the sidewinding at a steady speed of 1.5 m/s. Find: a) the magnitude of its resulting velocity with respect to the ground, b) the distance of his land fr
• Accelerated motion - mechanics
  The delivery truck with a total weight of 3.6 t accelerates from 76km/h to 130km/h in the 0.286 km long way. How much was the force needed to achieve this acceleration?
• The body
  The body slides down an inclined plane forming an angle α = π / 4 = 45° under the action of a horizontal plane under the effect of friction forces with acceleration a = 2.4 m/s ^ 2. At what angle β must the plane be inclined so that the body slides on it
• Up and down motion
  We throw the body from a height h = 5 m above the Earth vertically upwards v0 = 10 m/s. How long before we have to let the second body fall freely from the same height to hit the Earth at the same time?
• Average speed
  What is the average speed you have to move the way around the world in 80 days? (Path along the equator, round to km/h).
• Collision
  The two bodies, whose initial distance is 240 m, move evenly against each other consistently. The first body has an initial velocity of 4 m/s and an acceleration of 3 m/s², the second body has an initial speed of 6 m/s and an acceleration of 2 m/s². Fin
• Train 2
  The train slowed down from 90 km/h to 72 km/h in 5 seconds. How long track travel?
• A particle
  A particle moves in a straight line so that its velocity (m/s) at time t seconds is given by v(t) = 3t²-4t-4, t>0. Initially the particle is 8 meters to the right of a fixed origin. After how many seconds is the particle at the origin?
• Train speed
  The train speed is decreased during 50 sec from 72 km/h to 36 km/h. Assuming that the train movement is equally slowing, find the the acceleration and the distance that it travels at.
• An acceleration
  The car goes on a straight road at a speed of 72 km/h. At some point, the driver starts to brake and stops the car in 5 seconds. Find: (a) the acceleration during braking (b) the distance traveled during braking.