An axe is pushed against a grinding wheel consisting of a uniform disk of radius R = 0.250 m spinning at an initial angular velocity of ωi = 42.0 rad/s, resulting in a constant tangential frictional force of magnitude f = 7.00 N that causes the grinding wheel to come to a stop in Δt = 30.0 s (and the axe to get sharper). (a) Sparks of glowing metal fly off the axe with a speed equal in magnitude to the tangential velocity of the rim of the grinding wheel (and in a direction tangent to the wheel). Calculate the speed of the sparks when the wheel is turning at its initial angular velocity of ωi. (b) Find the angular acceleration α of the grinding wheel. (c) Through how many revolutions does the wheel turn before coming to rest? (d) Calculate the torque on the grinding wheel due to the force exerted by the axe (assume no other torques act other than the one caused by the axe). (e) Calculate the mass of the grinding wheel, assuming it to be a uniform disk. (f) Calculate the change in rotational kinetic energy of the disk during the first 5.0 s of grinding need answers to all parts

An axe is pushed against a grinding wheel consisting of a uniform
disk of radius R = 0.250 m spinning at an initial angular velocity of
ωi = 42.0 rad/s, resulting in a constant tangential frictional force of
magnitude f = 7.00 N that causes the grinding wheel to come to a
stop in Δt = 30.0 s (and the axe to get sharper).
(a) Sparks of glowing metal fly off the axe with a speed equal in
magnitude to the tangential velocity of the rim of the grinding
wheel (and in a direction tangent to the wheel). Calculate the
speed of the sparks when the wheel is turning at its initial angular velocity of ωi.
(b) Find the angular acceleration α of the grinding wheel.
(c) Through how many revolutions does the wheel turn before coming to rest?
(d) Calculate the torque on the grinding wheel due to the force exerted by the axe (assume no
other torques act other than the one caused by the axe).
(e) Calculate the mass of the grinding wheel, assuming it to be a uniform disk.
(f) Calculate the change in rotational kinetic energy of the disk during the first 5.0 s of grinding

need answers to all parts