Angular Acceleration and Projectile Motion

• MyNewPony
In summary, the conversation discusses a problem in which a marble is launched towards a cup in an amusement park game. The marble is placed on a spring-loaded wheel and released after making 11/12 of a revolution. The question asks for the necessary angular acceleration for the marble to land in the cup. The conversation provides equations and steps to find the launch velocity of the marble.
MyNewPony

Homework Statement

An amusement park game, shown in the figure (see attachment), launches a marble toward a small cup. The marble is placed directly on top of a spring-loaded wheel and held with a clamp. When released, the wheel spins around clockwise at constant angular acceleration, opening the clamp and releasing the marble after making 11/12 revolution.

What angular acceleration is needed for the ball to land in the cup?

Homework Equations

x1 = vcos(theta)t
y1 = y(initial) + vsin(theta)t - 4.9t^2

omega = v/r

a = (omega(final)^2 - omega(initial)^2)/2(delta(theta))

The Attempt at a Solution

1) 11/12 of a revolution = 330 degrees, therefore it is launched at an angle of 30 degrees.
2) It is shot from an initial height of rcos30 = 0.2*sqrt3/2 m
3) It has a range of 1 + rsin30 = 1 + 0.2*1/2 = 1.1 m

I know I'm supposed to find launch velocity from this data but how do I go about doing so?

Attachments

• Angular Acceleration.jpg
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MyNewPony said:

The Attempt at a Solution

1) 11/12 of a revolution = 330 degrees, therefore it is launched at an angle of 30 degrees.
2) It is shot from an initial height of rcos30 = 0.2*sqrt3/2 m
3) It has a range of 1 + rsin30 = 1 + 0.2*1/2 = 1.1 m
Sounds good. (I assume that the cup is at the same height as the center of the wheel? Hard to tell from the diagram.)

I know I'm supposed to find launch velocity from this data but how do I go about doing so?
Set up the usual projectile motion equations for vertical and horizontal position as a function of time.

I'm trying to do this same problem, but I don't know how. I was hoping I could figure it out with some online help, but I don't understand where you got all the equations and such.

1. What is angular acceleration?

Angular acceleration refers to the rate of change of angular velocity, which is the rate at which an object rotates around an axis. It is measured in radians per second squared (rad/s²).

2. How is angular acceleration related to projectile motion?

In projectile motion, the motion of an object can be broken down into horizontal and vertical components. The vertical component is influenced by the acceleration due to gravity, while the horizontal component remains constant. Angular acceleration comes into play when considering the rotation of the object around its axis, as well as the change in direction of the object's velocity.

3. What factors affect angular acceleration?

The main factors that affect angular acceleration are the moment of inertia, the torque applied to the object, and the distribution of mass within the object. The moment of inertia is a measure of an object's resistance to rotational motion, while torque is the force that causes an object to rotate.

4. How is angular acceleration calculated?

The formula for angular acceleration is α = Δω / Δt, where α is the angular acceleration, Δω (delta omega) is the change in angular velocity, and Δt (delta t) is the change in time. This formula can also be written as α = τ / I, where τ (tau) is the torque applied to the object and I is the moment of inertia.

5. How does angular acceleration differ from linear acceleration?

Angular acceleration refers to the change in rotational speed, while linear acceleration refers to the change in linear velocity. While linear acceleration is measured in units of distance per time squared (m/s²), angular acceleration is measured in units of radians per second squared (rad/s²).

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