10.3 Relating angular and translational quantities  (Page 4/5)

In circular motion, a tangential acceleration can change the magnitude of the velocity but not its direction. Explain your answer.

Suppose a piece of food is on the edge of a rotating microwave oven plate. Does it experience nonzero tangential acceleration, centripetal acceleration, or both when: (a) the plate starts to spin faster? (b) The plate rotates at constant angular velocity? (c) The plate slows to a halt?

At its peak, a tornado is 60.0 m in diameter and carries 500 km/h winds. What is its angular velocity in revolutions per second?

A man stands on a merry-go-round that is rotating at 2.5 rad/s. If the coefficient of static friction between the man’s shoes and the merry-go-round is ${\mu }_{\text{S}}=0.5$ , how far from the axis of rotation can he stand without sliding?

An ultracentrifuge accelerates from rest to 100,000 rpm in 2.00 min. (a) What is the average angular acceleration in ${\text{rad/s}}^2$ ? (b) What is the tangential acceleration of a point 9.50 cm from the axis of rotation? (c) What is the centripetal acceleration in ${\text{m/s}}^2$ and multiples of g of this point at full rpm? (d) What is the total distance travelled by a point 9.5 cm from the axis of rotation of the ultracentrifuge?

A wind turbine is rotating counterclockwise at 0.5 rev/s and slows to a stop in 10 s. Its blades are 20 m in length. (a) What is the angular acceleration of the turbine? (b) What is the centripetal acceleration of the tip of the blades at $t=0\text{s?}$ (c) What is the magnitude and direction of the total linear acceleration of the tip of the blades at $t=0\text{s?}$

What is (a) the angular speed and (b) the linear speed of a point on Earth’s surface at latitude $30\text{°}$ N. Take the radius of the Earth to be 6309 km. (c) At what latitude would your linear speed be 10 m/s?

A child with mass 30 kg sits on the edge of a merry-go-round at a distance of 3.0 m from its axis of rotation. The merry-go-round accelerates from rest up to 0.4 rev/s in 10 s. If the coefficient of static friction between the child and the surface of the merry-go-round is 0.6, does the child fall off before 5 s?

A bicycle wheel with radius 0.3m rotates from rest to 3 rev/s in 5 s. What is the magnitude and direction of the total acceleration vector at the edge of the wheel at 1.0 s?

The angular velocity of a flywheel with radius 1.0 m varies according to $\omega (t)=2.0t$ . Plot $a_{\text{c}}(t)\text{and}{a}_{\text{t}}(t)$ from $t=\text{0 to 3.0 s}$ for $r=1.0\text{m}$ . Analyze these results to explain when $a_{\text{c}}\gg a_{\text{t}}$ and when $a_{\text{c}}\ll a_{\text{t}}$ for a point on the flywheel at a radius of 1.0 m.