What is the net acceleration of the coin on a rotating disk?

In summary, a disk with a penny placed on it begins to rotate at a constant angular acceleration of 1.9 rad/s^2. At t=1.2 seconds, the net acceleration of the coin is found to be 14.51 m/s^2. However, there is an error in the calculation of the angular velocity, which should be 2.28 rad/s at t=1.2 seconds.
  • #1
ComputerForests000
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Homework Statement


A disk is initially at rest. A penny is placed on it at a distance of 1.4 m from the rotation axis. At time t=0s, the disk begins to rotate with a constant angular acceleration of 1.9 rad/s^2 around a fixed, vertical axis through it's center and perpendicular to it's plane. Find the magnitude of the net acceleration of the coin at t=1.2 seconds.

Homework Equations


tangential acceleration=α r
radial acceleration= r ω^2
ω = ω initial + α t

The Attempt at a Solution


I found the tangential acceleration to be 2.66 m/s^2,
then used ω = ω initial + α t to find the angular velocity, 3.192 m/s,
then found the radial acceleration to be 14.2644 m/s^2,
then took the square root of (tangential acceleration)^2 +(radial acceleration)^2 , which came out to be:
14.51 m/s^2
Apparently this answer is incorrect.
 
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  • #2
Something is wrong with the calculation of angular velocity (you also report it in units m/s which is also wrong), I calculated that is equal to 2.28 rad/s at time t=1.2s.
 
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  • #3
ComputerForests000 said:
to find the angular velocity, 3.192 m/s,
That's the tangential velocity, not the angular velocity.
 
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Related to What is the net acceleration of the coin on a rotating disk?

1. What is rotational kinematics?

Rotational kinematics is the branch of physics that studies the motion of objects that are rotating or spinning. It involves measuring and describing the position, velocity, and acceleration of an object as it rotates around a fixed axis.

2. What are the basic equations of rotational kinematics?

The basic equations of rotational kinematics are similar to those of linear kinematics, but they involve angular quantities instead of linear quantities. These include angular displacement, angular velocity, and angular acceleration, which are all measured in units of radians and radians per second.

3. How do I solve a rotational kinematics problem?

The steps to solving a rotational kinematics problem are similar to those of a linear kinematics problem. First, identify the known values and the unknown value. Then, select the appropriate equation to use and rearrange it to solve for the unknown variable. Finally, plug in the known values and solve for the unknown variable.

4. Can rotational kinematics be applied to real-life situations?

Yes, rotational kinematics can be applied to real-life situations. This branch of physics is used to study the motion of objects such as wheels, gears, and pendulums. It is also used in fields such as engineering, astronomy, and sports to analyze and design rotating systems.

5. What is the difference between rotational kinematics and rotational dynamics?

Rotational kinematics deals with the motion of objects that are rotating, while rotational dynamics involves the forces that cause this motion. In other words, kinematics focuses on describing the motion, while dynamics focuses on explaining the causes of the motion.

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