# physics

A string is wrapped around a uniform solid cylinder of radius r. The cylinder can rotate freely about its axis. The loose end of the string is attached to a block. The block and cylinder each have mass m. Note that the positive y direction is downward and counterclockwise torques are positive.

Find the magnitude, alpha, of the angular acceleration of the cylinder as the block descends.

Express your answer in terms of the cylinder's radius r and the magnitude of the acceleration due to gravity g.

1. 👍
2. 👎
3. 👁
1. Let T be the string tension. That and the angular acceleration alpha are the unknowns. Separate equations for the acceleration of the block and the angular acceleration of the cylinder will allow you to solve for both variables. The moment of inertia of the cylinder in (1/2) M r^2

m g - T = m a

T*r = torque = I*alpha = (1/2) m r^2 * alpha
T = (1/2) m*r*alpha

m g = ma + (1/2) m r * alpha
= ma + (1/2) m a
(since alpha = a/r)

a = (2/3) g
alpha = (2/3)(g/r)

1. 👍
2. 👎
2. Let T be the string tension. That and the angular acceleration alpha are the unknowns. Separate equations for the acceleration of the block and the angular acceleration of the cylinder will allow you to solve for both variables. The moment of inertia of the cylinder in (1/2) M r^2

m g - T = m a

T*r = torque = I*alpha = (1/2) m r^2 * alpha
T = (1/2) m*r*alpha

m g = ma + (1/2) m r * alpha
= ma + (1/2) m a
(since alpha = a/r)

alpha = (2/3) g
Note that the magnitude of the linear acceleration of the block is 23g , which does not depend on the value of r .

1. 👍
2. 👎

## Similar Questions

1. ### calc

When the height of a cylinder is 12 cm and the radius is 4 cm, the circumference of the cylinder is increasing at a rate of pie/4 cm/m in, and the height of the cylinder is increasing four times faster than the radius. How fast is

2. ### Physics

I need help with this question please. A solid cylinder of mass m and radius R has a string wound around it. A person holding the string pulls it vertically upward such that the cylinder is suspended in midair for a brief time

3. ### Physics - I just need help with c

I just need some clarification on part (c). Here's the whole problem for context: A uniform solid cylinder of mass 10 kg can rotate about a frictionless axle through its center O, as shown in the cross-sectional view in the

4. ### Physics

A small disk of radius R1 is mounted coaxially with a larger disk of radius R2. The disks are securely fastened to each other and the combination is free to rotate on a fixed axle that is perpendicular to a horizontal frictionless

1. ### Physics

Four objects - a hoop, a solid cylinder, a solid sphere, and a thin, spherical shell - each has a mass of 4.59 kg and a radius of 0.252 m. (a) Find the moment of inertia for each object as it rotates about the axes shown in the

2. ### physics

A uniform solid cylinder of radius R and a thin uniform spherical shell of radius R both roll without slipping. If both objects have the same mass and the same kinetic energy, what is the ratio of the linear speed of the cylinder

3. ### Algebra

This diagram shows a solid metal cylinder. The cylinder hasbase radius 2x and height 9x. The cylinder is melted down and made into a sphere of radius r Find an expression for in terms of x

4. ### Math

The diagram shows a solid metal cylinder. The cylinder has base radius 2x and height 9x. E cylinder is melted down and made into a sphere of radius r. Find the expression for r in terms of x.

1. ### Math

A solid body consists of a cylinder surmounted by a hemisphere of the same radius. The total length of the body, measured along the central axis of cylinder, is 10cm. If the radius of the hemisphere is xcm,show that the volume

2. ### Calculus

A solid is formed by adjoining two hemispheres to the ends of a right circular cylinder. The total volume of the solid is 2 cubic centimeters. Find the radius of the cylinder that produces the minimum surface area. (Round your

3. ### Physics

A uniform solid cylinder of mass 10 kg can rotate about a frictionless axle through its center. A rope wrapped around the outer radius R1 = 1.0 m exerts a force of magnitude F1 = 5.0 N to the right. A second rope wrapped around

4. ### physics

"A solid cylinder and a thin-walled hollow cylinder have the same mass and radius. They are rolling horizontally along the ground toward the bottom of an incline. They center of mass of each cylinder has the same translational