Problem 11 : The radius of the roll of paper shown in the figure (Figure 1) is 7.5 cm and its moment of inertia is I = 3.5×10−3 kg⋅m2 . A force of 2.5 N is exerted on the end of the roll for 1.0 s , but the paper does not tear so it begins to unroll. A constant friction torque of 0.12 m⋅N is exerted on the roll which gradually brings it to a stop. Part A Assuming that the paper's thickness is negligible, calculate the length of paper that unrolls during the time that the force is applied (1.0 s ). Express your answer using two significant figures. Part B Assuming that the paper's thickness is negligible, calculate the length of paper that unrolls from the time the force ends to the time when the roll has stopped moving.

The outstretched hands and arms of a figure skater preparing for a spin can be considered a slender rod pivoting about an axis through its center (Figure 1). When his hands and arms are brought in and wrapped around his body to execute the spin, the hands and arms can be considered a thin-walled hollow cylinder. His hands and arms have a combined mass 8.0 kg. When outstretched, they span 1.7 m; when wrapped, they form a thin- walled hollow cylinder of radius 23 cm. The moment of inertia about the rotation axis of the remainder of his body is constant and equal to 0.4 kg. m². For related problemsolving tips and strategies, you may want to view a Video Tutor Solution of Anyone can be a ballerina. Figure 1 of 1 TI Part A If his original angular speed is 0.50 rev/s, what is his final angular speed? Express your answer in revolutions per second. 15| ΑΣΦ W2 = 1.03 Submit Previous Answers Request Answer X Incorrect; Try Again; 8 attempts remaining Provide Feedback ? rev/s

5 A rigid body is undergoing planar motion with the velocity of its center of mass vc = 2 m/s i + 5 m/s j and an angular velocity of 10 rad/s k.  If a force of 10N i and a couple of 2 Nm k is applied to the body, what is the rate of its kinetic energy change with respect to time? 40 W 54 W 74 W 20 W

The triceps muscle in the back of the upper arm extends the forearm. This muscle in a professional boxer exerts a force of 2967 N with an effective perpendicular lever arm of 3.40 cm, producing an angular acceleration of the forearm of 130.0 rad / s². What is the moment of inertia of the boxer's forearm? moment of inertia: kg m? Question Credit: OpenStax College Physics

A solid uniform spherical boulder travels down a hill. At the top of the hill the boulder is rolling with a horizontal speed of 5 m/s. The top half of the hill is rough, so that the boulder continues to roll without slipping. The bottom half of the hill and the valley is covered in smooth ice, so that there is no static friction between the boulder and the hill. How fast is the boulder moving when it gets to the bottom of the hill? What is its rotational speed in the valley if the boulder has a radius of 10 cm? Rough 50.0 m Smooth

The fly wheel is an important mechanical element in machines that is used to increase the moment of inertia of the machine and store rotational kinetic energy. A fly wheel of an engine starts rotating about a fixed axis from rest to 102 rad/s in 6.3 seconds. The wheel has a radius of 0.5 meters and mass of 88 kg. Calculate the net torque acting on the fly wheel during the time interval t = 0; 6.3 s measured in Nm (Enter the number only).

A 270-g mass hangs from a string that is wrapped around a pulley, as shown in the figure. The pulley is suspended in such a way that it can rotate freely. When the mass is released, it accelerates toward the floor as the string unwinds. Model the pulley as a uniform solid cylinder of mass 1.00 kg and radius 5.00 cm. Assume that the thread has negligible mass and does not slip or stretch as it unwinds. Determine the magnitude a of the pulley's angular acceleration. 344 rad/s? Incorrect Determine the magnitude of the acceleration a of the descending weight. a = m/s? Question Source: Freedman College Physics 3e | Publ

The wheel of radius R shown below consists of a hoop of massm and two thin rods, each of mass M. Calculate the moment of inertia of the wheel about an axis going through its center, perpendicular to the plane of the hoop, for the values listed below. Express your answer in kg m2 to three significant figures. R= 2.28 m m = 0.372 kg M= 0.288 kg

The triceps muscle in the back of the upper arm extends the forearm. This muscle in a professional boxer exerts a force of 1559 N with an effective perpendicular lever arm of 3.25 cm, producing an angular acceleration of the forearm of 110.0 rad / s?. What is the moment of inertia of the boxer's forearm? moment of inertia: kg m?

A rope with a negligible mass has two blocks that are suspended over a pulley, m, and M, as shown in the image.  The pulley can be considered as a uniform solid cylindrical disk. What is the equation for the net torque on the disc? Assume acceleration of blocks are a=(1/2)(9.8m/s2). What is the moment of inertia for this shape? (using the net torque equation from the above question, substitute the moment of inertia) The angular acceleration is correlated to the linear acceleration as α=r. Make the substitution into the torque equation in order to get the equation in terms of acceleration, α only.