A thin, light string is wrapped around the rim of a 4.00 kg solid uniform disk that is 30.0 cm in diameter. A person pulls on the string with a constant force of 100.0 N tangent to the disk, as shown in Figure 10.48 . The disk is not attached to anything and is free to move and turn . (a) Find the angular acceleration of the disk about its center of mass and the linear acceleration of its center of mass. (b) If the disk is replaced by a hollow thin-walled cylinder of the same mass and diameter, what will be the accelerations in part (a)? Figure 10.48 Problem 13.
A thin, light string is wrapped around the rim of a 4.00 kg solid uniform disk that is 30.0 cm in diameter. A person pulls on the string with a constant force of 100.0 N tangent to the disk, as shown in Figure 10.48 . The disk is not attached to anything and is free to move and turn . (a) Find the angular acceleration of the disk about its center of mass and the linear acceleration of its center of mass. (b) If the disk is replaced by a hollow thin-walled cylinder of the same mass and diameter, what will be the accelerations in part (a)? Figure 10.48 Problem 13.
A thin, light string is wrapped around the rim of a 4.00 kg solid uniform disk that is 30.0 cm in diameter. A person pulls on the string with a constant force of 100.0 N tangent to the disk, as shown in Figure 10.48. The disk is not attached to anything and is free to move and turn. (a) Find the angular acceleration of the disk about its center of mass and the linear acceleration of its center of mass. (b) If the disk is replaced by a hollow thin-walled cylinder of the same mass and diameter, what will be the accelerations in part (a)?
Figure 10.48
Problem 13.
Definition Definition Rate of change of angular velocity. Angular acceleration indicates how fast the angular velocity changes over time. It is a vector quantity and has both magnitude and direction. Magnitude is represented by the length of the vector and direction is represented by the right-hand thumb rule. An angular acceleration vector will be always perpendicular to the plane of rotation. Angular acceleration is generally denoted by the Greek letter α and its SI unit is rad/s 2 .
A spool of wire of mass M and radius R is unwound under a constant force F (Fig. P10.85). Assuming the spool is a uniform solid cylinder that doesn’t slip, show that (a) The acceleration of the center of mass is 4F/3M and (b) The force of friction is to the right and equal in magnitude to F/3. (c) If the cylinder starts from rest and rolls without slipping, what is the speed of its center of mass after it has rolled through a distance d?
A spinning top with an initial moment of inertia of 0.3 kg•m? is rotating at an initial angular velocity of 8 rad/s. If the moment of inertia
decreases to 0.2 kg•m^2 while no external torques act on the system, what will be the final angular velocity of the top?
Suppose you start an antique car by exerting a force of 290 N on its crank for 0.13 s.
Variables:f = 290 Nt = 0.13 sd = 0.32 m
What angular momentum is given to the engine if the handle of the crank is 0.32 m from the pivot and the force is exerted to create maximum torque the entire time?
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