Problem 75
A soccer ball, which has a circumference of \(70.0 \mathrm{~cm}\), rolls \(14.0 \mathrm{~m}\) in \(3.35 \mathrm{~s}\). What was the average angular speed of the ball during this time?
Problem 76
After you pick up a spare, your bowling ball rolls without slipping back toward the ball rack with a linear speed of \(2.8 \mathrm{~m} / \mathrm{s}\) as shown in Figure \(8.28\). (a) If the diameter of the bowling ball is \(0.22 \mathrm{~m}\), what is its angular speed? (b) To reach the rack, the ball rolls up a ramp. If the angular speed of the ball when it reaches the top of the ramp is \(1.2 \mathrm{rad} / \mathrm{s}\), what is the linear speed of the ball?
Problem 77
Two forces produce the same torque. Does it follow that they have the same magnitude? Explain.
Problem 78
Does a larger force always produce more torque than a smaller force? Explain why not if your answer is no; give an example if your answer is yes.
Problem 80
A mechanic uses a wrench that is \(22 \mathrm{~cm}\) long to tighten a spark plug. If the mechanic exerts a force of \(58 \mathrm{~N}\) to the end of the wrench, what is the maximum torque she can apply to the spark plug?
Problem 82
A torque of \(0.97 \mathrm{~N} \cdot \mathrm{m}\) is applied to a bicycle wheel of radius \(35 \mathrm{~cm}\) and mass \(0.75 \mathrm{~kg}\). Treating the wheel as a hoop, find its angular acceleration.
Problem 83
Force to Hold a Baseball A person holds a \(1.42-\mathrm{N}\) baseball in his hand, a distance of \(34.0 \mathrm{~cm}\) from the elbow joint, as shown in Figure \(8.30\). The biceps, attached at a distance of \(2.75 \mathrm{~cm}\) from the elbow, exerts an upward force of \(12.6 \mathrm{~N}\) on the forearm. Consider the forearm and hand to be a uniform rod with a mass of \(1.20 \mathrm{~kg}\). (a) Calculate the net torque acting on the forearm and hand. Use the elbow joint as the axis of rotation. (b) If the net torque obtained in part (a) is nonzero, in which direction will the forearm and hand rotate?
Problem 84
At the local playground, a \(16-\mathrm{kg}\) child sits on the end of a horizontal teeter-totter, \(1.5 \mathrm{~m}\) from the pivot point. On the other side of the pivot an adult pushes straight down on the teeter-totter with a force of \(95 \mathrm{~N}\). In which direction does the teeter-totter rotate if the adult applies the force at a distance of (a) \(3.0 \mathrm{~m}\), (b) \(2.5 \mathrm{~m}\), or (c) \(2.0 \mathrm{~m}\) from the pivot? (Assume that the teeter-totter itself pivots at the center and produces zero torque.)
Problem 84
At the local playground, a 16-kg child sits on the end of a horizontal teeter- totter, \(1.5 \mathrm{~m}\) from the pivot point. On the other side of the pivot an adult pushes straight down on the teeter-totter with a force of \(95 \mathrm{~N}\). In which direction does the teeter-totter rotate if the adult applies the force at a distance of (a) \(3.0 \mathrm{~m}\), (b) \(2.5 \mathrm{~m}\), or (c) \(2.0 \mathrm{~m}\) from the pivot? (Assume that the teeter-totter itself pivots at the center and produces zero torque.)
Problem 85
A 25 -kg child sits on one side of a teeter-totter, at a distance of \(2 \mathrm{~m}\) from the pivot point. A mass \(m\) is placed at a distance \(d\) on the other side of the pivot, in an effort to balance the teeter-totter. Which of the following combinations of mass and distance (A, B, C, or D) balances the teeter-totter? (Assume that the teeter-totter itself pivots at the center and produces zero torque.) $$ \begin{array}{|l|l|l|l|l|} \hline & \text { A } & \text { B } & \text { C } & \text { D } \\ \hline \text { Mass, } \boldsymbol{m} & 10 \mathrm{~kg} & 50 \mathrm{~kg} & 40 \mathrm{~kg} & 20 \mathrm{~kg} \\ \hline \text { Distance, } \boldsymbol{d} & 2 \mathrm{~m} & 1 \mathrm{~m} & 1.5 \mathrm{~m} & 2.5 \mathrm{~m} \\ \hline \end{array} $$
