# Rotational Motion of a spun disk

• jeeves_17
In summary, to take a 200 g, 20-cm-diameter plastic disk from 0 to 1800 rpm in 4.0 seconds, the electric motor must supply a torque of 0.001 N*m. This can be found by calculating the angular acceleration and then using kinematics to find the torque.
jeeves_17
A 200 g, 20-cm-diameter plastic disk is spun on an axle through its
center by an electric motor. What torque must the motor supply to take
the disk from 0 to 1800 rpm in 4.0s? (Given: I = ½ MR2)

Relevant equations
I = 1/2 MR^2
T = Ia

The attempt at a solution
v=0.02m * 1800 rev/min / 4 sec * 60 sec / 1 min * 2 Pi / 1 Rev
v= 10 800 m/s

a = how do i get this?

I = 1/2 (0.2kg)(0.1)^2
I = 0.001

T = Ia
T = (0.001)a

is this correct?

What you need to compute is the angular acceleration ($\alpha$). Just like linear acceleration is defined as change in velocity over time, angular acceleration is change in angular velocity over time. What's the change in angular velocity? (Convert rpm to rad/s.)

Use kinematics w = wo + alpha*t. Here wo = zero and w = 2*pi*1800/60. From these values find alpha and then torque.

## 1. What is rotational motion?

Rotational motion is the movement of an object around its own axis. It is a type of motion where an object rotates or spins on a fixed point.

## 2. What is a spun disk?

A spun disk is a circular object that is rotated or spun around its central axis. It can be made of various materials such as metal, plastic, or even paper.

## 3. How does the rotational motion of a spun disk differ from linear motion?

The main difference between rotational motion and linear motion is the path of movement. In rotational motion, the object moves in a circular path around a fixed point, while in linear motion, the object moves in a straight line.

## 4. What factors affect the rotational motion of a spun disk?

The rotational motion of a spun disk is affected by various factors such as the mass, shape, and size of the disk, as well as the force applied to it, and the distance from the axis of rotation.

## 5. How is rotational motion of a spun disk used in real life?

The rotational motion of a spun disk has many practical applications, including the functioning of engines, turbines, and gears in machines. It is also used in everyday objects such as wheels, fans, and spinning tops.

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