A bug crawls around on a horizontal turntable rotating with constant angular speed ω. The massof the bug is m and the coefficient of friction of the bug with the surface of the turntable is µ.Recall that Fstatic friction ≤ |µN | where N = mg is the normal force. The onset of slippage occurswhen Fstatic friction = |µN |. Gravity points downward. Ignore non-inertial effects due to Earth’srotation.a) The bug crawls with constant speed vr relative to the turntable in a radial path. How farfrom the center of the turntable can the bug crawl before starting to slip (in terms of ω, µ,and g)?b) The bug crawls with constant speed vr relative to the turntable in a circular path of radius bon the turntable. The circular path is concentric with the center of the turntable. For whatvalue of vr (in terms of ω, b, µ and g) will the bug start to slip if it crawlsi) In the direction of rotation?ii) Opposite of the direction of rotation?

A 88.6 g drink is left on a turntable causing it to turn with an angular speed of 8.80 rad/s. If the drink has coefficients of friction of μs = 0.970 and μk = 0.470 with the turntable, what is the furthest distance that the drink could have been placed from the centre of the turntable for the drink not to slide? 0.0125 m 0.0595 m 0.00135 m 0.123 m

A small 𝑚𝑏 = 09.0 ∗ 10−3 bug stands at one end of a thin uniform bar that is initially at rest on asmooth horizontal table. The other end of the bar pivots about a nail driven into the table and canrotate freely, without friction. The bar has a mass of 𝑀𝑏𝑎𝑟 = 49.0 ∗ 10−3𝑘𝑔 and is 𝐿𝑏𝑎𝑟 =100. 𝑐𝑚 in length. The bug jumps off in the horizontal direction, perpendicular to the bar, with aspeed of 𝑣𝑏 = 21.0 𝑐𝑚𝑠 relative to the table. What is the angular speed of the bar just after the insectleaps? What is the total kinetic energy of the system just after the bug leaps? Where does thisenergy come from? (3 – sig figs)Problem 2The angular position 𝜃 of a 0.36m diameter flywheel is given by 𝜃 = (2.0 𝑟𝑎𝑑𝑠3 ) 𝑡3 . Find the 𝜃in radians and in degrees, at 𝑡1 = 2.0𝑠 and 𝑡2 = 5.0𝑠. (3 sig. figs)

A coin of mass 8.6 g is placed a distance 10.5 cm from the center of a horizontal turntable. The coefficient of static friction between the coin and the turntable is given as 0.52. The angular speed of the turntable is slowly increased until the coin slides off. Determine the maximum angular speed for which the coin stays in place. Express your answer in rad/s, to at least one digit after the decimal point.

A merry-go-round of radius R rotates at constant speed with period T. What minimum Co-effi-cient of static friction between merry-go-round and a box mass, m, placed at its edge the willenable the box to remain on the surface without sliding?

A small block of mass 200 grams moves with a uniform speed in a horizontal circulargroove. The radius of the groove’s vertical sidewalls is 50 cm. If the block takes 4.0 s tocomplete one round, find the normal force by the sidewall of the groove.