Question

A long string is wrapped around a 6.6-cm-diameter cylinder, initially at rest, that is free to rotate on an axle. The string is then pulled with a constant acceleration of 1.5m/s² until 1.3m of string has been unwound. If the string unwinds without slipping, what is the cylinder's angular speed in rpm, at this time?

mad = 1/2mv² + 1/2Iw² mad = 1/2mv² + 1/4mv² mad = 3/4mv² sqrt(4ad/3) = v Since w = v/r, then, sqrt(4ad/3) /r = w Since w * 60/2pi =rmp then, sqrt(4ad/3) /r *60/2pi = 466.6 rmp.

Answer 1

To find the cylinder's angular speed after 1.3m of string have been unwound, use the equations of rotational motion.

Step-by-step explanation:

To find the cylinder's angular speed after 1.3m of string have been unwound, we can use the equations of rotational motion.

Firstly, we need to find the linear velocity of the unwound string, which can be calculated using the formula v = sqrt(4ad/3), where v is the linear velocity, a is the constant acceleration, and d is the distance unwound.

Substituting the given values, we get v = sqrt(4 * 1.5 * 1.3) m/s.

The angular velocity is then determined by dividing the linear velocity by the radius of the cylinder, giving us w = v/r.

Finally, we convert the angular velocity from radians per second to revolutions per minute using the formula w * 60/2pi = rpm, resulting in an angular speed of 466.6 rpm.