cylindrical bar with a sphere firmly attached to one end is originally at rest in a horizontal position. The bar is pivoted about a free hinge at one end (Figure 8-61). The bar is 4.00 m long and has a mass of 231 kg. The sphere has a radius of 60.0 cm and a mass of 53.0 kg. A variable torque is applied to lift the bar by rotating it 37.0° about the pivot at a constant angular speed. Calculate the work done by the variable torque.

Find the torque about the point (1, −2, 1) due to the force F = 2i − j + 3k acting at the point (1, 1, −3).

An electric motor rotating a workshop grinding wheel at 1.08 x 10 rev/min is switched off. Assume the wheel has a constant negative angular acceleration of magnitude 2.06 rad/s? (a) How long does it take the grinding wheel to stop? Note that the time required for the wheel to stop is the same as the time for the wheel to start from rest and reach the given angular speed with the same magnitude angular acceleration, s (b) Through how many radians has the wheel turned during the time interval found in part (a)? It might be helpful to translate this problems into linear variables (a car traveling with an initial speed and then slowing down with a constant negative acceleration), rad Need Help? Road Master

A 250-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 9.00 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. rad/s? a = Determine the magnitude of the acceleration a of the descending weight. a = m/s? Calculate the magnitude of the tension T' in the string. T =

Problem 2: A wheel with radius r= 1.8 m has a tangential force F = 14.2 N acting on it as shown. F Part (a) What is the magnitude of the torque about the center of the wheel, in N•m? N•m sin() cos() tan() 7 8 9 НОMЕ cotan() asin() acos() E ↑^^| 4 5 6. atan() acotan() sinh() 1 3 cosh() tanh() cotanh() END O Degrees Radians VO BACKSPАСЕ DEL CLEAR Part (b) What is the direction of the torque?

A uniform, solid cylinder with mass M and radius 2R rests on a horizontal tabletop. A string is attached by a yoke to a frictionless axle through the center of the cylinder so that the cylinder can rotate about the axle. The string runs over a disk-shaped pulley with mass M and radius R that is mounted on a frictionless axle through its center. A block of mass M is suspended from the free end of the string (the figure (Figure 1)). The string doesn't slip over the pulley surface, and the cylinder rolls without slipping on the tabletop. Find the magnitude of the acceleration of the block after the system is released from rest. Express your answer in terms of g, M, R.

What is the angular acceleration and how long will it take to decrease rotational speed by 27 rad/s?

To develop muscle tone, a woman lifts a 2.00-kg weight held in her hand. She uses her biceps muscle to flex the lower arm through an angle of 60.0°. (a) What is the angular acceleration if the weight is 24.0 cm from the elbow joint, her forearm has a moment of inertia of 0.250 kg and the net force she exerts is 750 N at an effective perpendicular lever arm of 2.00 cm? (b) How much work does she do? m²

A 2.00-m long rod is hinged at one end. The rod is initially held in the horizontal position, and then released as the free end is allowed to fall. (a) What is the angular acceleration as it is released? (b) What is the angular acceleration when it reaches the vertical position? (c) Which position has the maximum angular velocity (vertical or horizontal)? (d) Which position has the maximum angular acceleration (vertical or horizontal)? (The moment of inertia of a rod about one end is ML2/3.)

A dragster starts from rest and accelerates down a track. Each tire has a radius of 0.320 m and rolls without slipping. At a distance of 393 m, the angular speed of the wheels is 253 rad/s. Determine (a) the linear speed of the dragster and (b) the magnitude of the angular acceleration of its wheels.