Chapter 4: Kinematics in Two Dimensions

I FIGURE EX4.36 shows the angular velocity graph of the crankshaft in a car. What is the crankshaft's angular acceleration at (a) $t=1\text{s}$, (b) $t=3\text{s}$, and (c) $t=5\text{s}$?

37. II FIGURE EX4.37 shows the angular acceleration graph of a turntable that starts from rest. What is the turntable's angular velocity at (a)$t=1\text{s}$ , (b) $t=2\text{s}$, and (c) $t=3\text{s}$?

38. II FIGURE EX4.38 shows the angular-velocity-versus-time graph for a particle moving in a circle. How many revolutions does the object make during the first 4 s?

. II A wheel initially rotating at experiences the angular acceleration shown in FIGURE EX4.39. What is the wheel's angular velocity, in rpm, at ?

FIGURE EX4.39

Answer Problems 3 through 5 by choosing one of the eight labeled acceleration vectors or selecting option $\text{I}:\overrightarrow{a}=\overrightarrow{0}$

4. At this instant, the particle is speeding up and curving upward. What is the direction of its acceleration?

A projectile is launched at an angle of ${30}^{°}$.

a. Is there any point on the trajectory where$\overrightarrow{v}$and$\overrightarrow{a}$are parallel to each other? If so, where?

b. Is there any point where$\overrightarrow{v}$and$\overrightarrow{a}$are perpendicular to each

other? It so, where?

A 5.0-m-diameter merry-go-round is initially turning with a $4.0\text{s}$period. It slows down and stops in $20\text{s}$.

a. Before slowing, what is the speed of a child on the rim?

b. How many revolutions does the merry-go-round make as it stops?

II An electric fan goes from rest to$1800\text{rpm}$ in $4.0\text{s}$. What is its angular acceleration?

A bicycle wheel is rotating at $50\text{rpm}$, and when the cyclist begins to pedal harder, giving the wheel a constant angular acceleration of $0.50\text{rad}/{\text{s}}^2$.

a. What is the wheel's angular velocity, in rpm, $10\text{s}$later?

b. How many revolutions does the wheel make during this time?

Starting from rest, a DVD steadily accelerates to $500\text{rpm}$in $1.0\text{s}$, rotates at this angular speed for $3.0\text{s}$, then steadily decelerates to a halt in $2.0\text{s}$. How many revolutions does it make?