A torsion pendulum consists of a metal disk with a wire running through its center and soldered in place. The wire is mounted vertically on clamps and pulled taut. Figure 15-58 a gives the magnitude τ of the torque needed to rotate the disk about its center (and thus twist the wire) versus the rotation angle θ . The vertical axis scale is set by τ s = 4.0 × 10 -3 N ·m. The disk is rotated to θ = 0.200 rad and then released. Figure 15-58 b shows the resulting oscillation in terms of angular position θ versus time t . The horizontal axis scale is set by t s = 0.40 s. (a) What is the rotational inertia of the disk about its center? (b) What is the maximum angular speed d θ / dt of the disk? ( Caution: Do not confuse the (constant) angular frequency of the SHM with the (varying) angular speed of the rotating disk, even though they usually have the same symbol ω . Hint: The potential energy U of a torsion pendulum is equal to 1 2 k θ 2 , analogous to U = 1 2 kx 2 for a spring.) Figure 15-58 Problem 97
A torsion pendulum consists of a metal disk with a wire running through its center and soldered in place. The wire is mounted vertically on clamps and pulled taut. Figure 15-58 a gives the magnitude τ of the torque needed to rotate the disk about its center (and thus twist the wire) versus the rotation angle θ . The vertical axis scale is set by τ s = 4.0 × 10 -3 N ·m. The disk is rotated to θ = 0.200 rad and then released. Figure 15-58 b shows the resulting oscillation in terms of angular position θ versus time t . The horizontal axis scale is set by t s = 0.40 s. (a) What is the rotational inertia of the disk about its center? (b) What is the maximum angular speed d θ / dt of the disk? ( Caution: Do not confuse the (constant) angular frequency of the SHM with the (varying) angular speed of the rotating disk, even though they usually have the same symbol ω . Hint: The potential energy U of a torsion pendulum is equal to 1 2 k θ 2 , analogous to U = 1 2 kx 2 for a spring.) Figure 15-58 Problem 97
A torsion pendulum consists of a metal disk with a wire running through its center and soldered in place. The wire is mounted vertically on clamps and pulled taut. Figure 15-58a gives the magnitude τ of the torque needed to rotate the disk about its center (and thus twist the wire) versus the rotation angle
θ
. The vertical axis scale is set by τs = 4.0 × 10-3 N ·m. The disk is rotated to
θ
= 0.200 rad and then released. Figure 15-58b shows the resulting oscillation in terms of angular position
θ
versus time t. The horizontal axis scale is set by ts = 0.40 s. (a) What is the rotational inertia of the disk about its center? (b) What is the maximum angular speed d
θ
/dt of the disk? (Caution: Do not confuse the (constant) angular frequency of the SHM with the (varying) angular speed of the rotating disk, even though they usually have the same symbol
ω
. Hint: The potential energy U of a torsion pendulum is equal to
1
2
k
θ
2, analogous to U
=
1
2
kx2 for a spring.)
Figure 15-58 Problem 97
Definition Definition Special type of oscillation where the force of restoration is directly proportional to the displacement of the object from its mean or initial position. If an object is in motion such that the acceleration of the object is directly proportional to its displacement (which helps the moving object return to its resting position) then the object is said to undergo a simple harmonic motion. An object undergoing SHM always moves like a wave.
A 95 kg solid sphere with a 15 cm radius is suspended by a vertical wire. A torque of 0.20 Nm is required to rotate the sphere through an angle of 0.85 rad and then maintain that orientation. What is the period of the oscillations that result when the sphere is then released?
A composite pendulum consisting of a uniform disk with radius R and mass 6m is connected to a uniform rod of length 6R and mass m according to the shape and oscillates in the gravitational field with low amplitude. What is the rotation period of the pendulum
A uniform slender rod of length L = 36 in. and weight W = 4 lb hangs freely from a hinge at A. If a force P of magnitude 1.5 lb is applied at B horizontally to the left (h = L), determine (a) the angular acceleration of the rod, (b) the components of the reaction at A.
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