A small rubber wheel is used to drive a large pottery wheel, and they are mounted so that their circular edges touch. The small wheel has a radius of 1.8 and accelerates at the rate of 7.0 , and it is in contact with the pottery wheel (radius 30.0 ) without slipping. Calculate the angular acceleration of the pottery wheel.

angular accelelatrion big wheel= 30/1.8 *7

I am not certain of your units.

To calculate the angular acceleration of the pottery wheel, we need to use the concept of torque. Torque is the rotational equivalent of force and is given by the equation:

Torque = Fr

Where F is the force and r is the radius. In this case, the force we are interested in is the force exerted by the small rubber wheel on the pottery wheel.

The torque exerted by the small wheel is equal to the torque exerted on the pottery wheel. Therefore, we can set up the equation:

Torque small wheel = Torque pottery wheel

The torque exerted by the small wheel can be calculated using the equation:

Torque small wheel = F * r_small

Where F is the force exerted by the small wheel and r_small is the radius of the small wheel.

The force exerted by the small wheel can be determined using Newton's second law for rotation:

F = I * α

Where I is the moment of inertia and α is the angular acceleration.

The moment of inertia for a solid disk is given by the equation:

I = (1/2) * m * r^2

Where m is the mass of the disk and r is the radius of the disk (small wheel).

To determine the mass of the small wheel, we can use its density, which is given as:

Density = Mass/Volume

Since the small wheel is a solid disk, its volume can be calculated using the formula for the volume of a cylinder:

Volume = π * r^2 * h

Where r is the radius of the small wheel and h is the height (thickness) of the small wheel.

Now, we have the equations for torque and moment of inertia in terms of the parameters given. We can substitute these equations into our initial equation to solve for the angular acceleration of the pottery wheel.