A small ball of mass 0.81 kg is attached to one end of a 1.70-m-long massless rod, and the other end of the rod is hung from a pivot. When the resulting pendulum is 20° from the vertical, what is the magnitude of the torque about the pivot? Number i Units N-m

A small ball of mass 0.81 kg is attached to one end of a 1.70-m-long massless rod, and the other end of the rod is hung from a pivot. When the resulting pendulum is 20° from the vertical, what is the magnitude of the torque about the pivot? Number i Units N-m

University Physics Volume 1

18th Edition

ISBN:9781938168277

Author:William Moebs, Samuel J. Ling, Jeff Sanny

Publisher:William Moebs, Samuel J. Ling, Jeff Sanny

Chapter10: Fixed-axis Rotation

Section: Chapter Questions

Problem 68P: A pendulum consists of a rod of mass 2 kg and length 1 m with a solid sphere at one end with mass...

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A uniform, hollow, cylindrical spool has inside radius R/2, outside radius R, and mass M (Fig. P10.47). It is mounted so that it rotates on a fixed, horizontal axle. A counterweight of mass m is connected to the end of a string wound around the spool. The counterweight falls from rest at t = 0 to a position y at time t. Show that the torque due to the friction forces between spool and axle is f=R[m(g2yt2)M5y4t2] Figure P10.47
Three identical thin rods, each of length L and mass m, are welded perpendicular to one another as shown in Figure P10.43. The assembly is rotated about an axis that passes through the end of one rod and is parallel to another. Determine the moment of inertia of this structure about this axis.
A pendulum consists of a rod of mass 2 kg and length 1 m with a solid sphere at one end with mass 0.3 kg and radius 20 cm (see the following figure). If the pendulum is released from rest at an angle of 30 , what is the angular velocity at the lowest point?
Figure P10.16 shows the drive train of a bicycle that has wheels 67.3 cm in diameter and pedal cranks 17.5 cm long. The cyclist pedals at a steady cadence of 76.0 rev/min. The chain engages with a front sprocket 15.2 cm in diameter and a rear sprocket 7.00 cm in diameter. Calculate (a) the speed of a link of the chain relative to the bicycle frame, (b) the angular speed of the bicycle wheels, and (c) the speed of the bicycle relative to the road. (d) What pieces of data, if any, are not necessary for the calculations? Figure P10.16
A pendulum consists ofa rod of mass 1 kg and length 1 m connected to a pivot with a solid sphere attached at the other end with mass 0.5 kg and radius 30 cm. What is the torque about the pivot when the pendulum makes an angle of 30 with respect to the vertical?
A long, uniform rod of length L and mass M is pivoted about a frictionless, horizontal pin through one end. The rod is nudged from rest in a vertical position as shown in Figure P 10.73. At the instant the rod is horizontal, find (a) its angular speed, (b) the magnitude of its angular acceleration, (c) the x and y components of the acceleration of its center of mass, and (d) the components of the reaction force at the pivot.
Review. A spool of wire of mass M and radius R is unwound under a constant force F (Fig. P10.42). Assuming the spool is a uniform, solid cylinder that doesnt 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?
If a loop of chain is spun at high speed, it can roll along the ground like a circular hoop without collapsing. Consider a chain of uniform linear mass density whose center of mass travels to the right at a high speed 0 as shown in Figure P16.67. (a) Determine the tension in the chain in terms of and 0. Assume the weight of an individual link is negligible compared to the tension, (b) If the loop rolls over a small bump, the resulting deformation of the chain causes two transverse pulses to propagate along the chain, one moving clockwise and one moving counterclockwise. What is the speed of the pulses traveling along the chain? (c) Through what angle does each pulse travel during the time interval over which the loop makes one revolution?
A simple pendulum consists of a small object of mass 3.0 kg hanging at the end of a 2.0-m-long light string that is connected to a pivot point. (a) Calculate the magnitude of the torque (due to the force of gravity) about this pivot point when the string makes a 5.0 angle with the vertical. (b) Does the torque increase or decrease as the angle increases? Explain. Figure P8.6
A uniform solid sphere of radius r is placed on the inside surface of a hemispherical bowl with radius R. The sphere is released from rest at an angle to the vertical and rolls without slipping (Fig. P10.81). Deter mine the angular speed of the sphere when it reaches the bottom of the bowl.
A potters wheel rotates with an angular acceleration = 4at3 3bt2, where t is the time in seconds, a and b areconstants, and has units of radians per second squared. Theinitial position of the wheel is 0 and the initial angular velocityis 0. Obtain expressions for the angular velocity and the angular displacement of the wheel as a function of time.
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