Centripetal Acceleration circular disk

In summary, the circular disk has a tangential acceleration of 30 cm/sec^2 and a centripetal acceleration of 0.3 rev/s. The formula for tangential acceleration is angular acceleration * radius, and the formula for centripetal acceleration is v^2/r, where v is equal to radius * angular velocity. The angular velocity is measured in radians/second.
  • #1
Simple Echo
4
0

Homework Statement


A circular disk of radius 30 cm is rotating with an angular acceleration of 1 radian/ s2. What is the tangential acceleration of a point on the rim of the disk? What is its centripetal acceleration if the angular speed is 3 rev / s?


Homework Equations


tangential acceleration = angular acceleration * radius



The Attempt at a Solution


tangential acceleration = 1 * 30 = 30 cm/sec^2

I'm not even sure I got that part right, my online reading just throws a bunch of random variables at me, and I have no idea what they're referring to. If someone could just explain the equation to me to figure out the Centripetal Acceleration, that would be great. I'm not asking you to do it, I just want to know how. I already failed at this question.
 
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  • #2
What formula did you use for centripetal acceleration?
 
  • #3
rock.freak667 said:
What formula did you use for centripetal acceleration?

That's one of my problems, I have no idea what the formula is to use.
 
  • #4
ac = v^2/r

So
Centripetal Acceleration = 3^2/30?
0.3 rev/s

I don't even think this is the right equation
 
  • #5
Simple Echo said:
ac = v^2/r

So
Centripetal Acceleration = 3^2/30?
0.3 rev/s

I don't even think this is the right equation

[tex]a_c=\frac{v^2}{r}[/tex]

but remember that v=rw so substitute that to get another form of centripetal acceleration.
 
  • #6
Velocity = Radius * W
What is the variable w?
 
  • #7
Simple Echo said:
Velocity = Radius * W
What is the variable w?

angular velocity
 

FAQ: Centripetal Acceleration circular disk

What is centripetal acceleration and how is it related to circular motion?

Centripetal acceleration is the acceleration that an object experiences when moving in a circular path. It is directed towards the center of the circle and is responsible for keeping the object on its circular path. Centripetal acceleration is related to circular motion because it is the acceleration that is necessary for an object to maintain a curved path instead of moving in a straight line.

How is centripetal acceleration calculated?

Centripetal acceleration can be calculated using the equation a = v²/r, where a is the centripetal acceleration, v is the velocity of the object, and r is the radius of the circular path. This equation shows that centripetal acceleration is directly proportional to the square of the velocity and inversely proportional to the radius of the circle.

What is the difference between centripetal acceleration and tangential acceleration?

Centripetal acceleration is the acceleration towards the center of a circular path, while tangential acceleration is the acceleration along the tangent of the circle. In other words, centripetal acceleration changes the direction of an object's motion, while tangential acceleration changes its speed.

How does the centripetal acceleration of a circular disk change with the radius?

The centripetal acceleration of a circular disk is inversely proportional to the radius. This means that as the radius increases, the centripetal acceleration decreases. This is because a larger radius results in a longer path, which means the object needs less acceleration to maintain its circular motion.

What are some real-life examples of centripetal acceleration in circular disks?

Some real-life examples of centripetal acceleration in circular disks include the rotation of a car's tires, the spinning of a merry-go-round, and the motion of a satellite orbiting around the Earth. In all of these cases, centripetal acceleration is responsible for keeping the object on its circular path.

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