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A $7\mathrm{.}5$ kg bowling ball is thrown horizontally at $3\mathrm{.}2\frac{m}{s}$ into a $4\mathrm{.}5$ kg cart that is initially at rest. The ball lands in the cart and sticks there. What is the momentum of the ball before it lands in the cart?

$($A$)24kg*\frac{m}{s}$

B$)16kg*\frac{m}{s}$

C$)32kg*\frac{m}{s}$

D$)48kg*\frac{m}{s}$

E$)72kg*\frac{m}{s}$

Referring to the question $1,$ what is the velocity of the cart after the ball lands in it$?$

$($D$)3\mathrm{.}2\frac{m}{s}$

B$)6\mathrm{.}0\frac{m}{s}$

C$)4\mathrm{.}8\frac{m}{s}$

D$)7\mathrm{.}2\frac{m}{s}$

E$)2\mathrm{.}0\frac{m}{s}$

Starting from rest, two skaters push off against each other on ice where friction is negligible. One is a $50$ kg woman and one is a $90$ kg man. The woman moves away with a speed of $+3\mathrm{.}6\frac{m}{s}.$ What is the initial momentum of the system?

$($A$)180kg*\frac{m}{s}$

B$)324kg*\frac{m}{s}$

C$)140kg*\frac{m}{s}$

$($D$)0kg*\frac{m}{s}$

A bicycle travels $141$ m along a circular track of radius $30$ m $.$ What is the angular displacement in radians of the bicycle from its starting position?

$141$ m

A$)1\mathrm{.}0$ rad

B$)1\mathrm{.}5$ rad

C$)3\mathrm{.}0$ rad

$($D$)4\mathrm{.}7$ rad

E$)9\mathrm{.}4$ rad

A wheel with a $0\mathrm{.}10-m$ radius is rotating at $35re\frac{v}{s}.$ It then slows uniformly to $15re\frac{v}{s}$ over a $3\mathrm{.}0-$s interval. What is the angular acceleration of a point on the wheel?$-$

$C$

A$)-2\mathrm{.}0re\frac{v}{s^2}$

B$)0\mathrm{.}67re\frac{v}{s^2}$

C$)6\mathrm{.}7re\frac{v}{s^2}$

D$)42re\frac{v}{s^2}$

E$)-17re\frac{v}{s^2}$

During the spin$-$dry cycle of a washing machine, the motor slows from $90ra\frac{d}{s}$ to $30ra\frac{d}{s}$ while the turning the drum through an angle of $180$ radians. What is the magnitude of the angular acceleration of the motor?

A$)64ra\frac{d}{s^2}$

$($B$)32ra\frac{d}{s^2}$

C$)10ra\frac{d}{s^2}$

D$)20ra\frac{d}{s^2}$

E$)1\mathrm{.}0ra\frac{d}{s^2}$

An airplane engine starts from rest; and $2$ seconds later, it is rotating with an angular speed of $420re\frac{v}{m}in.$ If the angular acceleration is constant, how many revolutions does the propeller undergo during this time?

A$)7$

B$)14$

C$)21$

D$)49$

E$)150$

A gymnast on a high bar swings through two revolutions, which is equal to

A$)3\mathrm{.}15$ rad $.$

B$)6\mathrm{.}30$ rad $.$

C$)9\mathrm{.}45$ rad $.$

$($D$)12\mathrm{.}6$ rad.

A centimeter ruler, balanced at its center point, has two coins placed on it$,$ as shown in the figure. One unknown mass $M_1$ is placed at the zero mark; the other mass $M_2=0\mathrm{.}10kg$ is placed at the $4\mathrm{.}7$ cm mark. The center of the ruler is at the $3\mathrm{.}0$ cm mark. The ruler is in equilibrium; it is perfectly balanced. Taking the axis of rotation at the center, what is the torque due to weight of $M_2?$

A$)-0\mathrm{.}017$ Nm

$($B$)0\mathrm{.}17$ Nm

C$)0\mathrm{.}017$ Nm

D$)-0\mathrm{.}17$ Nm

$r=Fl$

What is the mass $M_1$ in question $11?$ Hint: Use condition of static equilibrium.

A$)57$ kg

B$)5\mathrm{.}7$ kg

C$)0\mathrm{.}57$ kg

$($D$)0\mathrm{.}057$ kg