A particle moves in a circle of radius $a$ at constant speed $v$. Find the angular speed and the magnitude of the acceleration.

A particle moves $3.0 \mathrm{~m}$ along a circle of radius $1.5$ $\mathrm{m}$. (a) Through what angle does it rotate? (b) If the particle makes this trip in $1.0 \mathrm{~s}$ at a constant speed, what is its angular velocity? (c) What is its acceleration?

Two points are on a disk that is turning about a fixed axis perpendicular to the disk and through its center at increasing angular velocity. One point is on the rim and the other point is halfway between the rim and the center.

$(d)$ Which point has the greater angular speed?

Two points are on a disk that is turning about a fixed axis perpendicular to the disk and through its center at increasing angular velocity. One point is on the rim and the other point is halfway between the rim and the center.

$(e)$ Which point has the greater tangential acceleration?

Two points are on a disk that is turning about a fixed axis perpendicular to the disk and through its center at increasing angular velocity. One point is on the rim and the other point is halfway between the rim and the center.

$(a)$ Which point moves the greater distance in a given time?

Two points are on a disk that is turning about a fixed axis perpendicular to the disk and through its center at increasing angular velocity. One point is on the rim and the other point is halfway between the rim and the center.

$(g)$ Which point has the greater centripetal acceleration?

Two points are on a disk that is turning about a fixed axis perpendicular to the disk and through its center at increasing angular velocity. One point is on the rim and the other point is halfway between the rim and the center.

$(f)$ Which point has the greater angular acceleration?

Two points are on a disk that is turning about a fixed axis perpendicular to the disk and through its center at increasing angular velocity. One point is on the rim and the other point is halfway between the rim and the center.

$(c)$ Which point has the greater speed?

Two points are on a disk that is turning about a fixed axis perpendicular to the disk and through its center at increasing angular velocity. One point is on the rim and the other point is halfway between the rim and the center.

$(b)$ Which point turns through the greater angle?

A particle moves 3.0 m along a circle of radius 1.5 m. (a) Through what angle does it rotate? (b) If the particle makes this trip in 1.0 s at a constant speed, what is its angular velocity? (c) What is its acceleration?

A pilot with a mass of $50 \mathrm{~kg}$ comes out of a vertical dive in a circular arc such that at the bottom of the arc her upward acceleration is $3.5 g.$(a)$ How does the magnitude of the force exerted by the airplane seat on the pilot at the bottom of the arc compare to her weight?

A pilot with a mass of 50 kg comes out of a vertical dive in a circular arc such that at the bottom of the arc her upward acceleration is 3.5g.

(b) Use Newton’s laws of motion to explain why the pilot might be subject to a blackout. This means that an above normal volume of blood “pools” in her lower limbs. How would an inertial reference frame observer describe the cause of the blood pooling?

A 0.20-kg stone is whirled in a horizontal circle on the end of an $0.80$-m-long string. The string makes an angle of $20^{\circ}$ with the horizontal. Determine the speed of the stone.

The coefficient of static friction between a rubber tire and the road surface is $0.85$. What is the maximum acceleration of a $1000-\mathrm{kg}$ four-wheel-drive truck if the road makes an angle of $12^{\circ}$ with the horizontal and the truck is

$(b)$ descending?