Angular and linear velocity

In summary, the roller with a diameter of 0.44 m rolls down a slope starting from rest and completing 6 rotations in 12 seconds. To calculate the angular velocity at the end, we need to use the kinematic equations for rotational motion under constant acceleration. The linear velocity at the end cannot be determined without knowing the radius of the slope. The angular acceleration can be calculated by using the equation omega = (2*pi)/t, where t is the time for one rotation. The linear acceleration can be calculated using the equation a = r*alpha, where alpha is the angular acceleration. Finally, the distance travelled can be calculated by multiplying the number of rotations by the circumference of the roller.
  • #1
aghakarim
3
0
5. A roller 0.44 m diameter rolls down a slope starting from rest. It takes 12 seconds make 6 complete rotations along the sloping surface accelerating uniformly as it moves. Calculate the following:

(1). The angular velocity at the end.

(2). The linear velocity at the end.

(3). The angular acceleration.

(4). The linear acceleration.

(5). The distance travelled.




from the question its obvious each rotation takes two seconds

12/6=2
then i thought omega= (2*pi)/12 gives you rads per second
but i then got really confused as i actualy don't have the velocity in the question and i lost it all

is the angular velocity (number of revs*2*pu)/number of cycle?

any ideas? i am losttt!
 
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  • #2
Start from the kinematic equations for rotational motion. Although 12/6 is always equal to 2, this is irrelevant here. Each complete revolution takes less time as the roller accelerates down the incline. Furthermore, the angular velocity also changes as time increases.
 
  • #3
but wouldn't all reveloutions be the same since the rollers speed is the same and in move uniformly?
 
  • #4
also is this equation right to work out the final velocity?

v=2*pi*r/t

then the answer times the number of rotation?
or more needs to be done or is this wrong?
 
  • #5
aghakarim said:
but wouldn't all reveloutions be the same since the rollers speed is the same and in move uniformly?
The roller's speed is not the same at all times. It starts from rest and this means that its initial velocity is zero. If the roller's velocity were the same at all times, its velocity would remain at zero and the roller would stay where it is, at the top of the incline. This is not what happens. The roller rolls down the incline which means that its velocity changes from zero to something other than zero. Therefore the roller accelerates and this means that its velocity is not the same at all times.
also is this equation right to work out the final velocity?

v=2*pi*r/t
It is not right because it assumes that the acceleration is zero, i.e. that the roller makes the same number of revolutions in the same amount of time. As I just pointed out, the acceleration cannot be zero.

Like I said, what are the kinematic equations for rotational motion under constant acceleration? There are four of them. Write them down and see whether you can figure out which one to use considering what is given to you.
 

What is the difference between angular and linear velocity?

Angular velocity is the rate of change of angular displacement with respect to time, while linear velocity is the rate of change of linear displacement with respect to time. In simpler terms, angular velocity measures how quickly an object is rotating, while linear velocity measures how quickly an object is moving in a straight line.

How are angular and linear velocity related?

Angular and linear velocity are related through the formula v = rω, where v is the linear velocity, r is the radius of the circle, and ω is the angular velocity. This means that as one increases, the other also increases, and vice versa.

What are some real-life applications of angular and linear velocity?

Angular and linear velocity are used in many applications, such as in the design of gears, machinery, and vehicles. They are also important in sports, such as in measuring the speed of a rotating ball in baseball or the speed of a spinning figure skater.

How is angular velocity measured?

Angular velocity is typically measured in radians per second (rad/s) or degrees per second (deg/s). It can be measured using a device called an accelerometer, which measures the rate of change of angular displacement, or by using a tachometer, which measures the number of revolutions per unit time.

What factors affect angular and linear velocity?

The factors that affect angular and linear velocity include the initial velocity, the acceleration, the radius of rotation, and any external forces acting on the object. Additionally, the mass and distribution of mass of the object can also affect its angular and linear velocity.

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